Ridly Greig and Brady Tkachuk scored for the Senators (32-22-9), who went 4-0-1 on a five-game road trip while improving to 5-0-2 during the seven-game streak and 9-1-2 in the past 12.
Tim Stutzle had an assist to extend his point streak to 13 games (17 points; eight goals, nine assists).
Ottawa was playing its first game of the season without No.1 defenseman Jake Sanderson, who is out week to week with an upper-body injury sustained at the Seattle Kraken on Saturday.
Kevin Lankinen made 22 saves for the Canucks (19-37-8), who have one win in their past 10 games (1-6-3) and three in the past 26 (3-18-5).
It was the first shutout of the season for Reimer, who signed as a free agent with Ottawa on Jan.12 after sitting out the first half of the season, and his 32nd in the NHL.
Reimer made his best saves off rush chances, stopping Liam Ohgren on a 2-on-1 at 5:04 of the first period, and making a glove save on a close-range Max Sasson shot off a breakaway from the hash marks at 6:23 of the second.
Greig put Ottawa ahead 1-0 at 10:11 of the second period after Artem Zub’s quick point shot hit Shane Pinto high and bounced right to Greig alone in the slot, where he made a nice move to pull the puck from his backhand to forehand before firing a shot past Lankinen’s blocker.
Vancouver challenged for a missed stoppage because the puck hit Pinto in the glove as he tried to protect his face, but a video review deemed it a deflection and not a hand pass.
Tkachuk scored into an empty net at 18:40 of the third period to make it 2-0 and extend his point streak to seven games (seven points; three goals, four assists). Stutzle assisted to keep his streak alive.
