The Vancouver right-winger scored his first and second goals of an injury-marred season as the Canucks defeated the Winnipeg Jets 3-2 in a shootout Wednesday night.
Chris Higgins had the only goal in the shootout as Vancouver (30-28-10) handed the Jets (30-28-9) their fifth straight loss.
Burrows was playing in only his 36th game this season after breaking a foot to start the season and then breaking his jaw in December.
"I hit a few posts, a few saves, a few rebounds, a few empty nets that should have gone in," Burrows said. "It's a fine line between goals and not.
"Tonight I was able to get a few. Even though, honestly, I could have got four, I think. I hit the post, a few tips that they blocked and a two-on-one in the first my stick breaks."
But Vancouver suffered another injury blow when centre Ryan Kesler left the game in the second period after a knee-on-knee collision with Jets centre Jim Slater.
Canucks head coach John Tortorella said Kesler will be sent back to Vancouver for tests while his teammates keep travelling to games against Washington, Florida and Tampa Bay.
"He's going to get some imaging and we'll have a better indication of where he's at, but he's out for a while," Tortorella said.
Slater said he didn't intentionally try to hurt Kesler.
"I thought I had him lined up, he kind of bailed there at the last second there," Slater said. "I didn't stick my knee out or anything in his path, wasn't leading with my leg. I thought I actually took the worst of it.
"Obviously, if he's hurt bad, I feel bad about that. It wasn't any intent. I thought I had him lined up and at the last second he tried to jump out of the way."
Higgins scored the decisive goal with some quick stick-handling on his way toward Ondrej Pavelec, flipping the puck by him after the netminder went down.
Andrew Ladd scored his 18th goal of the season and Michael Frolik added his 13th that put the Jets ahead 2-1 early in the third period.
Burrows had tied the game 2-2 at 11:17 of the third period.
Vancouver is now 2-4-1 in their last seven games.
The game was a big improvement for the Canucks, who collapsed on Monday and gave up seven goals in the third period in a 7-4 loss to the New York Islanders.
Pavelec stopped 30 of the 32 shots he faced in regulation and overtime, while Eddie Lack made 31 saves for Vancouver.
Lack had let in six goals in the embarrassing loss to the Islanders.
"I just needed a big bounce-back game and I was really happy we got the win," Lack said.
The Canucks now have 70 points and Winnipeg 69 as they battle for a playoff spot in the Western Conference. Dallas holds the last wild-card berth with 74 points. Phoenix has 73. The Stars and Coyotes were idle Wednesday night.
The Jets are 0-2-3 in their last five and host the New York Rangers on Friday.
"We got opportunities to get the second point there the last couple games. We've got to start getting them," said Jets rookie defenceman Jacob Trouba, who logged almost 28 minutes of ice time.
"Those are points we're letting slip away. It's good that we get one and we look at the positives and try to think about that, but at the same time it's at the back of your mind — you've got to get those points that you're letting go."
Vancouver outshot Winnipeg 14-9 in the scoreless first period, but the Jets outshot the Canucks 16-5 in the third.
Vancouver was 0 for 5 on the power play and the Jets went 0 for 4.
"I thought we played hard right on through, and that's two out the last three games we've played well in the third period so good for them," Tortorella said.
"They've hung in, they've hung together. Losing a big guy like Kes, I thought they stuck together as a group. It was real nice to see."
Notes: Henrik Sedin was marking a major milestone, playing in his 1,000th NHL game, all with Vancouver. He was drafted third overall by the Canucks in the 1999 NHL Entry Draft.