Alex Formenton (2) and Parker Kelly scored for Ottawa while Filip Gustavsson stopped 34 shots in the Ottawa net (29-41-7). Vancouver (38-28-11) had goals from J.T. Miller, Brock Boeser, Travis Dermott while Jaroslav Halak made 14 saves before he was replaced by Thatcher Demko to start the second period who would turn aside 14 shots.
"It was really nice to get two [goals] and it was even better for us to pull off that win," Formenton said.
After overtime had solved nothing, it took until the fifth round of the shootout to decide the victor. Drake Batherson had kept Ottawa alive as he scored in round three after Miller had converted the round previous and after Connor Garland and Brady Tkachuk were unsuccessful in the fourth round, Gustavsson stopped Nic Petan before Adam Gaudette buried the shootout-winner against his former team.
"I had a move in mind, I stuck with it and it went in," he said.
The win was the 1,000th regular season victory in Senators history. Ottawa is 1,000-980-115-176 all-time.
"We kept battling and we got better as the game went on," Sens head coach D.J. Smith said. "Everyone involved, that's a great, gutsy, win."
Despite being outshot 14-10, the Canucks came out of the first with a two-goal lead thanks in large part to their power play.
With Dylan Gambrell in the box, Vancouver took a 1-0 lead just 1:55 in as Miller used a Boeser screen to bury his 30th. The lead was doubled at 15:14 and it came seconds after a Zach Senyshyn penalty expired as Boeser scored his 21st as the Sens forward was attempting to get back into the play.
Formenton's first of the night got Ottawa on the board at 4:04 of the second as he tipped in a Nikita Zaitsev point shot.
Kelly's sixth of the season made it 2-2 at 2:17 of the third as after Erik Brannstrom's blast went wide, the puck hit the backboards and bounced out front to Kelly who saw his shot hit the bar but then deflect off Demko's back and into the net.
Ottawa had its first lead of the night at 3:49 as Formenton blew past Luke Schenn before he lifted the puck high for his second multi-goal game of the season. Vancouver made it 3-3 at 6:47 on Dermott's first as a Canuck as he was wide open in the slot to bury Boeser's centering pass.
"We got down early but we stayed with it," Smith said. "It was a really good effort."
Ottawa completes its three-game road trip Friday night in Columbus. Puck drop is 7 p.m.