Nashville Predators coach Peter Laviolette said he didn't see Burrows' hit on centre Paul Gaustad.
All that mattered was the Canucks killed off a long power play that stretched into overtime and pulled out a shootout win over the Predators.
Nick Bonino and Radim Vrbata scored in the shootout, and the Canucks beat the Predators 5-4 Tuesday night to avoid being swept by Nashville.
"We responded well," Desjardins said. "We used up a lot of gas trying to get the kills, and we found a way to get the kills. After that we were kind of spread out on who was playing with who.
"I thought the guys battled the whole night, and it looked like there were a lot of really, really good things out of this game."
The Canucks padded their lead to four points over Calgary for second place in the Pacific Division with their second win in two nights. They will wait and see if Burrows gets any further punishment for appearing to hit Gaustad high with his shoulder.
Burrows said he thought they collided, and he didn't intend to hurt Gaustad.
There was no update on Gaustad's condition after the game.
"I hope he's all right," Burrows said. "It was a big win by the boys. They battled hard and found a way to kill that major, and it was a big win."
Eddie Lack stopped all four Nashville shots in overtime, then turned away attempts by Mike Santorelli and Filip Forsberg in the shootout. Vrbata beat Pekka Rinne with a backhander for the win.
Burrows had a goal and an assist before he was ejected. Chris Higgins, Linden Vey and Jannik Hansen scored a goal each, and Bonino had two assists.
Mike Fisher, Cody Franson, Taylor Beck and Viktor Stalberg scored for Nashville, which lost its second straight at home. The Predators pulled within two points of NHL-leading Anaheim (105) in the Western Conference with both teams having four games remaining.
Vancouver led 4-3 after scoring twice in the first six minutes of the third period before Fisher tied it with a power-play goal at 14:57.
The Predators got their big chance after Burrows' high hit on Gaustad with 3:54 left in regulation.
Lack stopped shot after shot to get the Canucks to overtime, and finished with 34 saves.
"That's a huge opportunity to win the game, and we had a couple chances," Nashville defenceman Roman Josi said. "We've just got to find a way to score a goal there."
Vancouver has started its final road trip in style, building off a 4-1 win at St. Louis on Monday. Desjardins started Lack for the second straight game, trying to give his club a tighter grip on its position in the standings.
Franson scored his first goal since being traded back to Nashville on Feb. 15, putting the Predators ahead 1-0. Bieksa checked Stalberg in the head, leaving Stalberg on the ice for a couple of minutes before he skated to the bench.
Fisher got the puck to Franson, who scored from the blue line at 4:30 of the first against the NHL's third-best road penalty-killing unit.
Nashville was 2 of 7 with the man advantage.
The Predators quickly made it 2-0 when Gaustad found Beck skating toward the offensive zone with a pass, and Beck finished off the rush by beating Lack glove-side with a snap shot at 8:15 of the first.
The Canucks erased that lead in the second as Vey scored his 10th on a snap shot that slid under Rinne at 4:04. Hansen netted his 15th during 4-on-4 play at 6:04.
After Nashville hit a couple of goal posts, Stalberg put the Predators up 3-2 with 29.4 seconds left in the second with a shot from the right circle that went in off Lack's shoulder.
Burrows tied it with a short-handed goal at 1:23. Nashville had the man advantage again when Craig Smith was sent to the box for interfering with Higgins, giving Vancouver the power play that Higgins finished with his 12th goal.
NOTES: Higgins has five points in five games for the Canucks. ... Nashville finished 6-7-2 in March. Vancouver was 10-4-2. The Canucks are 5-2 in the shootout this season. Nashville fell to 6-6. ... Stalberg has five points (two goals, three assists) in his last eight games.