A shot from the high slot by Jeff Carter deflected off the body of Scott Hartnell and into the net, snapping a 2-2 tie with a little over 12 minutes left. Danny Briere kept the puck in the zone and fed Carter to set up the goal, Hartnell's third in his last 24 games.
With the win, the Flyers climbed from seventh to fifth in the Eastern Conference. It was their first win in Dallas since 1996, ending a 0-4-2 drought.
Gagne had a goal - his eighth in the last 10 games - and an assist.
Boucher, in his first start since Dec. 21, made 27 saves - including a sensational stop on Karlis Skrastins in front with 9 minutes, 20 seconds left - and was flawless after the first period.
If there was any uneasiness in the Flyers' locker room because Boucher will be their goaltender for at least the rest of the regular season, it wasn't evident before Thursday night's game.
Asked if he sensed the loss of another injured goalie had put the Flyers in a mental funk, coach Peter Laviolette was succinct with his answer.
"If we go down that route and start feeling sorry for ourselves, we'll be out of the playoffs pretty quick," he said before the game. "You need to fight for what you want."
What they want is a high playoff seeding. (And, if they are being honest, a first-round matchup that doesn't include Pittsburgh or Washington.)
"You need to play good hockey down the stretch. If we don't, we'll be in trouble," Laviolette said. "If we do, then we'll know we'll make the playoffs and have an opportunity to play for the Stanley Cup. The ball's in our court."
They played an uneven first period and fell into a 2-1 hole because Dallas left winger Steve Ott netted a pair of goals.
The first goal, scored with Ryan Parent in the penalty box for tripping, went inside the right post from the high slot. Boucher seemed to have a clear view of the shot.
