Defenseman Michal Kempny scored twice for Washington in 2:44 in the third period to tie the game, and Nicklas Backstrom scored the deciding goal in the third round of the tiebreaker.
"I feel like these types of moments, they build the team spirit and build the team together, and that's huge for us," said Evgeny Kuznetsov, who scored his second goal of the night with 0.3 seconds left in the second period to get the Capitals within 5-2. "We stick with each other, we stick to the game plan even though the game never went well, we give up some bad goals, but we stick with our plan, and we get the results."
[WATCH: All Capitals vs. Canucks highlights]
Lars Eller had a goal and an assist, and Ilya Samsonov made 29 saves for the Capitals (8-2-3), who rebounded from blowing a two-goal lead in the third period and losing 4-3 in overtime to the Edmonton Oilers on Thursday. They are 5-0-1 in their past six.
Washington's John Carlson (five goals, 13 assists) and Alex Ovechkin (eight goals, five assists) each had his point streak end at nine games.
"[Ovechkin and Carlson] have carried us for a long time," coach Todd Reirden said. "But what happens in these back-to-backs is you need to have other guys step up."
Video: WSH@VAN: Kuznetsov beats Markstrom from in tight
Tim Schaller scored two goals, and Jacob Markstrom made 24 saves for the Canucks (6-3-1), who lost for the second time in eight games.
"That's not good enough," captain Bo Horvat said. "Going in with a four-goal lead, 21 minutes left, we've got to be able to hold those. We've got to be a lot better than that in the third. … At times, I think guys -- including myself -- were trying to make plays out of nothing and not getting the pucks in deep and simplifying our game. And I think that's what turned on us."
Eller set up Kuznetsov's goal late in the second and scored shorthanded at 1:57 of the third to make it 5-3.
"A little more life, a little more hope in the locker room at the end and built that up going into the third period," Eller said of Kuznetsov's second goal. "Get one late, get one early, and now it's a game."
Kempny scored on point shots through traffic that made it 5-4 at 4:57 and tied it 5-5 at 7:41.
"It didn't go as we expected, but I love that we didn't give up," he said. "Huge comeback win for us."
Kuznetsov scored alone in tight at 3:18 of the first period to put the Capitals ahead 1-0, but Brock Boeser tied it 1-1 on the power play off a pass from Quinn Hughes at 5:33.
Schaller scored on a shorthanded rush at 7:29 to put the Canucks ahead 2-1.
Elias Pettersson made it 3-1 with a wrist shot from inside the right face-off circle at 5:59 of the second, and Schaller batted a loose puck out of the air to make it 4-1 at 13:39.
Schaller has three goals, matching his total in 47 games last season.
"I still think I have a lot more to give," he said. "But it's nice to see hard work paying off, and I'm going to keep working hard and hopefully good things keep happening."
Jake Virtanen put the Canucks ahead 5-1 with a quick shot from the slot at 14:54.
Carlson leads the NHL with 21 points (five goals, 16 assists) in 13 games. With one game left this month, he is four points from tying the NHL record for most points by a defenseman in October, set by Al MacInnis with the Calgary Flames in 1990.
Video: WSH@VAN: Backstrom wins shootout for Capitals
They said it
"That goal at the end of the second was huge. Just a little bit of life, and then we said we needed to get another one early, and we did that, and then after that it was just a big push. We have been on the wrong side of a couple of those games, and it was nice to be on the other side. It was big for the character of the team going forward." -- Capitals forward Lars Eller on Evgeny Kuznetsov scoring with less than one second left in the second period
"Give their team credit, they've been through these games many times. They're a big, strong team. You could see it in certain areas of the game where I thought we lost a few puck battles and certain situations. Again, they're built to win Stanley Cups, and we can learn a lot from this game." -- Canucks coach Travis Green
Need to know
Carlson was one game shy of tying the Capitals record for longest point streak by a defenseman, shared by Robert Picard (Dec. 17, 1978-Jan. 9, 1979) and Al Iafrate (Nov. 25-Dec. 12, 1992). ... It was the fifth time in Capitals history that they came back from down four goals to win a game and first since a 5-4 overtime victory at the New York Rangers on Dec. 23, 2008. ... Washington forward Travis Boyd made his season debut, replacing Chandler Stephenson in the lineup, and provided a screen on each Kempny goal. He also had an assist on Kempny's second. ... Hughes, a rookie defenseman, has an assist on each of the four power-play goals the Canucks have scored in three games since he was moved on to the top unit.
Capitals: At the Toronto Maple Leafs on Tuesday (7 p.m. ET; TSN4, NBCSWA, NHL.TV)
Canucks: Host the Florida Panthers on Monday (10 p.m. ET; ESPN+, SNP, FS-F, NHL.TV)
Video: Capitals rally to beat Canucks in shootout