Wyatt Johnston stole the puck from Senators defenseman Jake Sanderson and fed Seguin in front, where he scored with a snap shot glove side on Anton Forsberg for his first goal in 10 games.
"[Johnston] makes the play, right, a second effort to get the puck back," Stars coach Pete DeBoer said. "A great play by a young guy. If he wasn't our best forward, he was in that conversation, so he deserved to be out there."
Miro Heiskanen scored twice, Nils Lundkvist had a goal and an assist, and Jake Oettinger made 28 saves for Dallas (15-7-5), which won beyond regulation for the first time in six tries this season.
Lundkvist tied it 3-3 at 14:54 of the third period with a knuckling point shot that deceived Forsberg.
"It wasn't our best," Seguin admitted. "Like I said, it wasn't my best. We just found a way to win tonight."
Thomas Chabot scored for the third straight game, and Forsberg made 28 saves for Ottawa (10-14-2).
"Down 2-0 early, and not a couple of great goals [against], but stayed with it and battled," Senators coach D.J. Smith said. "I thought we played a really good game. To lose that way in overtime, it hurts, but in saying that, that's a really good team and we had all kinds of opportunities to win."