Gaudette pointed to goalie coach Ian Clark for his shootout skills.
''I have to give credit to (Clark) who gave me a couple of shootout ideas last year, and in practice the other day we were working on it as well. I just had a move in my mind and stuck with it,'' said Gaudette, who deked around Filip Gustavsson and tucked it inside the near post.
Bo Horvat had a goal and an assist, Brock Boeser also scored in regulation and Thatcher Demko made 30 saves for Vancouver.
''He seems so confident in there,'' Gaudette said about Thatcher. ''I knew Thatcher many years ago and I could always tell he was something special and it's great to see him really coming out and playing well. He's huge for us right now and he's only gonna get better.''
The Canucks have won three straight - also beating Ottawa 3-2 in overtime Monday night - and six of seven to improve to 15-16-3.
Ryan Dzingel and Josh Norris scored for the Senators. They lost goaltender Joey Daccord to an injury in the third period.
''I thought we battled hard to get it back to 2-2,'' Senators coach D.J. Smith. ''That game could go either way. It's unfortunate we don't win.''
Daccord, who had his first NHL victory Sunday against Toronto, left at 5:07 of the third period. He appeared to twist a knee when he went down in the net, and grimaced while being helped off the ice. Filip Gustavsson took over for his NHL debut.
''It was kind of perfect. You don't have to think about it. You just jump straight into the game,'' Gustavsson said.
The Senators acquired goaltender Anton Forsberg off waivers from from Winnipeg earlier in the day to shore up its goaltending depth with both top netminder Matt Murray (upper-body injury) and Marcus Hogberg (lower-body injury) sidelined.
Boeser opened the scoring at 2:29 of the first with his 15th of the season, and Horvat added his 13th on a 2-on-1 tap-in at 8:26 of the period. Dzingel drew Ottawa within a goal three minutes into the second, and Norris tied it at 5:34 of the third.
Canucks: At Montreal Friday and Saturday nights.
Senators: Host Calgary on Monday and Wednesday nights.
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