Parker Kelly scored, and Korpisalo made 27 saves for the Senators (16-24-1), who lost for the seventh time in nine games (2-6-1).
"I thought that was probably the first game that we stuck with the gameplan, and we were patient," Ottawa interim coach Jacques Martin said. "Even after two (periods), we're down one and we felt it's going to come and it did and we got a goal and tied it. We had some opportunities."
Appleton gave the Senators a 1-0 lead at 14:35 of the second period when he took a centering pass from Nino Niederreiter on a 3-on-1 rush and beat Korpisalo glove side with a wrist shot from the slot. Appleton has scored in back-to-back games after not scoring in 25 straight games.
"Give us credit for finding a way to win the game even though I would say we weren't at our best," Jets coach Rick Bowness said. "But 'Helly' is going to make the timely saves, and 'Nik' is going to get that timely goal. We get the two points and move on."
Kelly tied it 1-1 at 4:43 of the third period when he one-timed a centering pass from Vladimir Tarasenko in the slot.
"The whole game, we didn't give them much," Kelly said. "It was a really good game and I thought we deserved a better fate."
Ottawa forward Josh Norris had an assist in 20:04 of ice time in his return after missing four games with an upper-body injury.
"I thought we played a good game," Norris said. "They've got a good team and don't give you much. For 60 minutes, I thought we played a good game. A guy makes a really good play in overtime and that's the game."
NOTES: Hellebuyck allowed two or fewer goals against in 10 consecutive games for the second time this season (also Nov. 17-Dec. 16). He became the ninth different goaltender in NHL history to post multiple double-digit streaks with two or fewer goals against in a single season and the third in the modern era (since 1943-44), joining Marc-Andre Fleury (2007-08, Pittsburgh Penguins) and Harry Lumley (1953-54, Toronto Maple Leafs). … Winnipeg is 13-1-3 against the Eastern Conference this season. ... Niederreiter (434) tied Mark Streit for the second-most points by a Switzerland-born player in NHL history. Roman Josi is first (641). … Ottawa center Shane Pinto is eligible to return against the Philadelphia Flyers on Sunday after serving a 41-game suspension for activities relating to sports wagering. He signed a one-year contract on Friday.