Matt Murray made 12 saves before being replaced by Marcus Hogberg in the second period as the Swede stopped 18 shots. Colin White and Evgenii Dadonov scored for the Senators (17-27-4). Vancouver's (19-19-3) Brayden Holtby turned away 26 shots as Nate Schmidt, Brock Boeser, Tanner Pearson and J.T. Miller had goals.
"I thought we played good enough to probably get a point," Sens head coach D.J. Smith said. "We just played a little too wide open when the game was tied and it cost us."
The hosts took a 1-0 lead just 1:43 in as Schmidt fired home a one-timer after taking advantage of a White turnover in his own zone.
White would redeem himself at 8:32 as after Josh Brown's shot was saved, White was on hand out front to score on the rebound after outmuscling Jake Virtanen for his ninth of the season.
After taking a tripping penalty, Murray left the game with 15:33 to play in the second and was replaced by Hogberg, who was promptly beaten on the man advantage 19 seconds later on Boeser's 17th of the year.
"Very unfortunate," Smith said of his goaltending situation. "Forsberg was scheduled to start but got hurt warming up. Then, Murray goes in and he got hurt and then we're down to Hoggy who practiced today.
"Things happen in the NHL and you've got to adjust."
The Senators were unable to convert on a double-minor after Virtanen was penalized for high-sticking at 11:27, but their best opportunity came through Alex Formenton who was slashed by Tyler Myers on a breakaway at 15:51 resulting in the Sens' first penalty shot of the season but the rookie couldn't convert.
Dadonov tied the game with 8:08 to play in regulation on an end-to-end rush as he beat Holtby from the left circle as his shot slightly changed direction after hitting Myers' stick but the Canucks re-took the lead 1:53 later as Pearson used Thomas Chabot as a screen on an odd-man rush to make it 3-2.
Miller scored into the empty-net to complete the scoring with less than a minute to play.
The Sens' six-game streak of scoring a power play goal came to an end tonight as they went 0-for-6 on the man advantage.
"They played it well," Chabot said of the Canucks' penalty kill. "Last game we scored a few on them and we obviously knew they were going to tighten things up … and you've got to give them some credit. But, at the same time, this is the power play and we want to be the difference in the game and we want to be out there and score some goals … and it's something we want to get right back on track with."
Anton Forsberg suffered a lower-body injury while warming up for the game while Murray left the game with a lower-body injury.
Smith revealed post-game that Sens forward Artem Anisimov was the next goaltender in line if he was needed.
"We had Arty dressed and ready to go," Smith said.
Ottawa concluded its four-game road trip with a 3-1 record that featured wins over Montreal, Calgary and Vancouver.
"Coming on the road like that, getting three wins out of four ... in the big picture you've got to be happy with the way the road trip went," Chabot said.
Ottawa and Vancouver will meet again Monday night at Canadian Tire Centre.
