Elias Pettersson had a goal and an assist, Quinn Hughes had two assists, and Braden Holtby made 36 saves and had an assist for the Canucks (5-5-0). Vancouver had lost five of its previous six games before outscoring the Senators 16-3 to win three straight for the first time this season.
"The three games here were really big just to get things back on track before things really slide," Hughes said. "I think our team has a high standard and everyone wants to win, so we can get down on each other fast, but we pick each other up and to win this series is a good step in the right direction."
Thomas Chabot scored, and Matt Murray made 21 saves for the Senators (1-6-1), who are 0-6-1 since winning their season opener.
Ottawa players expressed frustration following a 5-1 loss Wednesday, but coach D.J. Smith said he saw more positives in their game Thursday.
"We didn't win tonight, but that's our best effort of the three games, for sure," Smith said. "We worked away from the puck, we worked on keeping the chances down, we were better in our defensive zone. It's unfortunate we don't win tonight, but if we play that hard every night, we're going to start to win games."
Boeser put the Canucks ahead 1-0 on the power play at 5:30 of the first period, carrying the puck from the side of the net to the top of the crease unchecked before spinning and shooting it back the other way past Murray's blocker.
"It was a three-game set that we needed to reset," Boeser said.