Cody Ceci and Ryan Dzingel scored in regulation for the Senators (1-0-2).
Thomas Vanek scored for the Canucks and played a role in Chris Tanev's goal. Henrik Sedin had two assists for Vancouver (1-0-1).
Canucks goaltender Jacob Markstrom stopped 40 shots, while the Senators' Craig Anderson made 26 saves.
Dzingel used a pretty feed from Bobby Ryan to tie the game 2-2 at 5:09 of the third. Ryan was parked on the far boards when he sent a pass through the crease that Dzingel put into the top of the net.
Vancouver's Sven Baertschi had the best chance in the three-on-three overtime but was stopped on a breakaway by Anderson.
For the second consecutive game, Markstrom gave up an easy goal early in the first period.
The game was just 4:08 old when Ceci took an innocent-looking shot from the faceoff circle that hit Markstrom's glove then trickled into the net between his pads to give Ottawa a 1-0 lead.
The Canucks tied the game at 7:03 when Tanev fired a shot through traffic that Anderson didn't see. The goalie was partly screened by Vanek, who was parked in front of the net.
The Canucks were outshot 15-8 in the second period but managed to take a 2-1 lead on Vanek's goal.
Sedin won the faceoff and sent the puck to Troy Stecher, who passed it to Vanek. The left winger launched a shot from the high slot that found the far corner of the net behind a screened Anderson at 14:28. It was Vanek's first goal as a Canuck since signing as a free agent in September.
NOTES: C Henrik Sedin helped set up Vancouver's first goal by banking the puck off the back of the Senators' cage. ... RW Brock Boeser, who led Vancouver with four goals and seven points in the exhibition season, was a healthy scratch for the second consecutive game. ... Other Canucks scratches were D Alex Biega and D Derrick Pouliot. ... Vancouver's homestand continues Thursday against Winnipeg. ... Ottawa RW Alex Burrows, who spent 12 seasons in Vancouver before being traded to Ottawa on Feb. 27, was honored with a video tribute. ... Senators D Erik Karlsson missed his third straight game after June 14 foot surgery. ... D Johnny Oduya missed his second game with a lower-body injury. ... Ottawa dressed seven defensemen. ... Ottawa's road trip continues with games in Calgary on Friday and Edmonton on Saturday.