Mark Stone, William Karlsson and Jack Eichel also scored for the Golden Knights. Logan Thompson stopped 38 shots to earn his 11th win, second-most in the NHL.
Jake Sanderson got his first career goal for Ottawa with his father in attendance, and Cam Talbot made 32 saves.
Carrier scored his seventh of the season - his career high is nine - when he skated through the neutral zone, dangled his way past two Senators in the offensive zone and fired an off-balance wrist shot far side to give Vegas a 2-1 lead at 16:23 of the second period.
Not that the seventh-year veteran could remember any of it, though.
''A little bit of a blackout. I have to recheck it,'' Carrier said with a smile. ''But I've been hot right now so confidence is high and we're playing pretty well. ... But Karly had to steal my highlight there with his own highlight one, so I might not make it to the clips here tonight.''
To Carrier's point, Karlsson made it 3-1 when he lasered a beautiful backhand with his back to Talbot off a spin move from the left dot for his fifth of the season at 2:39 of the third.
''I think I've seen Karly do special things like that. But Will, he's playing awesome,'' Vegas defenseman Brayden McNabb said. ''He's been a rock star for us. He's so hard to play against, even in practice, and now he's showing it in games. I couldn't be happier for him.''
Eichel's backhand from the red line into an empty net with 1:41 left provided the final margin.
The Golden Knights solidified their place atop the Western Conference standings with 33 points heading into Thanksgiving, generally a benchmark for NHL teams. According to the Elias Sports Bureau, 76% of teams in playoff position on Thanksgiving went on to reach the postseason from 2005-06 through 2018-19, the last season not affected by the pandemic.
''It's relevant, otherwise they wouldn't bring it up every year,'' Vegas coach Bruce Cassidy said. ''Still think we've got a lot of things we've got to do better. But again tonight, one of the things we've done well is find ways to win.''
Vegas is looking to return to the playoffs after missing out for the first time last season.
Stone opened the scoring on a power play when he took Eichel's no-look pass and fired a shot into the net. It was his ninth goal of the season and Eichel's 15th assist.
Ottawa also got on the board with a man advantage, when Sanderson's drive from the blue line deflected slightly off Vegas defenseman Alec Martinez's stick and past Thompson to tie it.
''It felt nice,'' Sanderson said. ''Took a while, but I'm happy I got it and I'm grateful my dad could be there to watch it, so it's pretty cool.''
NOTES: Eichel has at least one point in 16 of Vegas' first 21 games. ... Playing in his 900th career game, Golden Knights defenseman Alex Pietrangelo got his team-high 18th assist of the season. ... Sanderson became the first Montana-born skater in NHL history to score a goal. ... With his assist on Sanderson's goal, Tim Stutzle became Ottawa's franchise leader in points before the age of 21 with 106.
Senators: Visit the Anaheim Ducks on Friday.
Golden Knights: Host the Seattle Kraken on Friday.
More AP NHL: https://apnews.com/hub/NHL and https://twitter.com/AP-Sports
Copyright 2023 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.