Kes from the Places of Exile timeline saving all of Fluidic Space from a Voth doomsday weapon with her telepathic powers.
P8 Blue might have one for saving a planet from a disease-bearing missile by landing on said missile, crawling along it, hijacking its controls and riding it back out into space.
Corbin Entek entirely deconstructing Iliana Ghemor and reminding us why Cardassians are the finest monologuers in the galaxy.
Do the Ships of the Line calendars count as part of the Expanded Universe? If this is the case, click here, start the movie (You are impatient? Start at 8:20!), and get ready for a true nerd-gasm!
Scotty in Indistinguishable from Magic saves the crew of the Challenger and the Romulan Tomalak's Fist all the while knowing that he's dying from heart failure brought on by being blasted through the galactic barrier and the century he spent in transporter stasis. In the middle of it all, just to keep himself occupied while the plan comes together, he works a way out of what looks like a "no chance of survival" situation. Even Spock admits that although logic says Scotty is dead, there is a possibility that he isn't, and Scotty is a master in finding the slimmest of possibilities. Basically, Scotty is so awesome, he makes probability his bitch.