This is essentially the plot of Yellow Submarine, with The Beatles being called upon to save a magical land from the music-hating Blue Meanies.
Quite a few of George Pal's Puppetoons. "Tulips Shall Always Grow" ends with a folk dance that reverses the effects of an invasion of goose-stepping robots!
One editor said it best in her review of Rock & Rule: "A dark magician old-arse rock star's wicked plans are thwarted by Furries who sing early 80's rock music. Yes, that is the actual plot." To be more specific, the Power of Rock can summon a demon, and the Power of Love can send it back — specifically, the power of Debbie Harry of Blondie and Robin Zander of Cheap Trick singing a duet together.
Kidd Video, a cavalcade of strangeness about a rock band pulled into a land of magic by an Evil Overlord who wants to control all music.
Also parodied in Shrek, where Princess Fiona's high note is enough to make the friendly bird singing with her explode in a puff of feathers. Oops.
Shrek the Third had Snow White summon animals with her usual Disney-like singing, then stare down the Huorns guarding the city gates as the metal intro to Led Zeppelin's "The Immigrant Song" plays. She then does the musical screaming into, which launches the animals to attack the Huorns.
One of Plankton's evil plans involved a rock band and unedited music.
Parodied in Family Guy. Three words: KISS Saves Santa.
The South Park episode "Die Hippie, Die" involves Cartman dispersing a huge crowd of hippies using a Slayer CD.
The Real Ghostbusters episode "Play Them Ragtime Boos" involved the guys facing off with a bunch of ghosts whose swing music turned time back to The Roaring '20s... Yes, the boys played Rock and Roll. With specially-programmed instruments and a visual trip from fifties to eighties. (Yes, folks, Egon's hair got more insane.)
Cobra tried this once in G.I. Joe by having the Dreadnoks form a band called "Cold Slither" and use Mind-Control Music. (Not exactly their brightest idea, becoming a popular rock band that the whole country knows about with a name that's pretty obvious.)
Aku tried something similar to that in the Samurai Jack episode "Jack and the Rave Slaves".
The Aqua Teen Hunger Force Colon Movie Film For Theatres has Neil Peart, the legendary drummer/songwriter of Rush, raise Meatwad from the dead by performing the "Solo of Life". Tongue-in-cheek promotional material published before the movie's release suggested that the solo would be the climax of the film and would run 45 minutes long. In fact, it's closer to 45 seconds.
There's also the episode "Revenge of the Mooninites", where the Mooninites trick Meatwad into helping them acquire the Foreigner Belt, which gives the wearer super-powers based on songs by the rock group Foreigner. We get to see "Dirty White Boy"note Makes Meatwad act like a redneck, "Cold as Ice"note Freezes Carl in a block of ice "Double Vision"note Gives Frylock double vision, and "Hot Blooded"note Makes the water in Carl's pool boil, scaring off the Mooninites. Then Carl accidentally inflicts "Head Games"note Turns his head into a Connect Four board on himself.
Carl: "I don't need no instructions to know how to Rock!"
And then there's Rock-A-Doodle (which Don Bluth fans normally do NOT like to talk about). The movie is a very loose re-imagining of the tale of Chanticleer, the singing rooster who believes he alone summons the sunlight with his voice. In this case, Chanticleer is an Elvis Expy who (very) gradually learns that his golden tones are the only thing that can stop an evil wizard owl who wants to plunge the world into eternal nighttime.
Metalocalypse is all about this trope. Death Metal band Dethklok rock so hard they can raise ancient Finnish trolls and cause volcanoes to erupt. They also have billions of crazed fans worldwide and their music seems to be gradually destroying civilisation.
The "Crush My Battle Opponent's Balls" music video has Skwisgaar killing dragons with his music, possibly in homage to the Yngwie Malmsteen artwork from the page image.
In Storm Hawks, the villainess Ravess built a massive sonic cannon that channeled the sound of her orchestra into blasts that could blow ships out of the sky. The heroes countered this by converting their hangar into an amp that similarly channeled Finn's electric guitar. The result can only be described as a Rock vs. Classical Beam-O-War.
In Chuck Jones' lovely adaptation of George Seldon's A Cricket in Times Square, Chester, the titular musical Orthopteran, saves a tiny newsstand after he learns he has a talent for playing classical music. In the finale, Chester plays his last "concert", a musical farewell to the city. All of the jaded New York City residents, every one of them, stop to listen. The sequence is illustrated almost entirely with Jones' own sensitive sketches of the City, and it's one of the most downright moving moments in animation.
Lest we forget, Hammerman. (In this case, it's the power of dancing, but it still counts.)
In the Duck Dodgers episode "In Space No-One Can Hear You Rock", the Martians use the power of easy-listening jazz against Earth. Dodgers enlists the help of Dave Mustaine of Megadeth to destroy their saxaphone-ray. See for yourself.
British TV series Freefonix is set in the future, where, apparently, The Power of Rock can be used to make the musician fly, control people's minds, and reverse time.
The ReBoot episode "Talent Night" featured a guitar battle that faked the viewers out. Megabyte enters the stage and pops out of a coffin, sinister-looking musical equipment unfolds seemingly out of nowhere, and he turns his guitar to eleven. Bob confronts him, with Glitch taking the form of a guitar, and they have an epic rock fight. Then, after it's over... Megabyte hands his guitar to Enzo, says "I've always wanted to do that," and leaves peacefully.
In Transformers Animated, Soundwave can use music to control machines and can also overwhelm with the sheer volume of the sound. The show's version of Laserbeak transforms not into a tape, but a guitar and he can hack into computers (as well as mind-control both humans and robots). And when he shows up, it is awesome.
Sari: I've heard your music, Soundwave. I'm not impressed. Soundwave: I have upgraded my instruments. * he plays a power chord on Laserbeak that sends Sari hurtling into the far wall*
And did we mention the guitar duel between Soundwave and Optimus Prime at the end of the episode?
Soundwave: Your axe is useless, Autobot. Optimus Prime: But yours isn't!
The original Transformers had the episode "Carnage in C Minor". This featured a planet of beings who could use music as a weapon, which catered to original flavor Soundwave's musical abilities. It's also regarded as one of the worst episodes in the entire franchise.
More thanks to its horrendously Off Model animation - at one point, Brawn and Huffer (who are dead) are shooting at a rocket engine, alongside Bonecrusher (who helped build it).
In Sonic Underground, not only were the characters in a rock band, their main weapons were their instruments.
In their "Cliptastic Countdown", Phineas and Ferb pulled it off by performing their extended version of "Gitchee Gitchee Goo" to save everyone who had been brainwashed by Dr. Doofenshmirtz's own music video.
The KaBlam!! episode "Your Logo Here!" was about the main duo trying to make the show more educational, and bring in a Barney-esque otter, "Ed the Educational Otter". His teachings made the kids nuts, and Henry ended up trapping him. The lure? His electric guitar solo.
The Teen Titans couldn't beat Punk Rocket as the sonic waves from his guitar stopped all attacks until Beast Boy had him play so loud the sound system blew.
There was an episode of Alvin and the Chipmunks where they demolished the Berlin Wall and ended the Cold War through the power of a rock ballad. It was All Just a Dream, but a prophetic one. After the song, Alvin woke up to find the Wall still in place; he sadly muses, "So it was only a dream... But it doesn't have to be." Ironically this cartoon aired about eleven months before the real Berlin Wall came down.
In an episode of Squidbillies, Rusty sells his soul to Satan for the ability to be a better guitar player than his dad. Cue the ensuing power rock duel where Early unleashes the full power of his skill, playing so fast it reaches into the ultrasound range, easily outdoing his son's demon-powered solo. It turns out Early had struck a similar bargain with Satan, so it ends as hell on earth anyway.
The Regular Show episode "This Is My Jam". To combat an extremely catchy song come alive, Mordecai and friends form a band and sing their own Ear Worm to blast it. This results in manifesting two ethereal rockers who use their guitars as swords.
In Joe Horne's series of 1-minute animated shorts "Stevie and Zoya," which debuted on MTV in the late 1980s, there is a scene where the title characters blast rock and roll from a boombox to rescue a group of people who have been turned into disco zombies and turn them back into themselves.
My Little Pony: Equestria Girls – Rainbow Rocks is all about this. It starts with a school-wide musical showcase, and when the siren-esque villains hear about it, they manage to turn into an all-out Battle of the Bands to feed off the developing hostilities of the student body, and only the protagonists' five-girl rock band can have any hope of saving the day.
Metalocalypse likes to play with this. In one of the first episodes, Dethklok manages to summon an ancient Finnish demon, the Mustakrakish, which proceeds to lay waste to all of Finland. Later in the series, they play on top of a dormant volcano, which somehow erupts anyway, killing off the entire audience...
Furthermore, Dethklok themselves are the most successful band in the world, being the 12th largest economy by the end of season 1, meaning they earn more money than Belgium and a lot of other countries! All because they make awesome music, and has a few billion fans.
In Gravity Falls, zombies can be destroyed by a perfect three-part harmony. Cue Mabel, Dipper and Stan singing karaoke in the wake of a Zombie Apocalypse.
Camp Lakebottom: In "The Great Tiki Hunt", McGee overcomes the evil Tiki god with the power of a ukelele solo.
In Julius Jr., there are times where the power of rock is the solution to the problem the gang is facing, notably in the episode Rock Sitting when Worry Bear's sentient rock collection goes missing and the only way to draw them out is the power of music.