Vancouver (45-27-5) remained in second place in the Pacific Division with 95 points; Nashville (47-22-9) is atop the Central Division with 103 points.
"I thought we played real well," Canucks coach Willie Desjardins said. "I thought they played hard early but I thought we really battled. We found a way to battle in the second, and then the third was a battle. They're a tough team to play. We were under siege quite a bit with our (defense), they were getting pressure. I thought we played hard the whole night."
The Canucks had to kill a five-minute penalty with 3:54 remaining and 1:06 into overtime after forward Alexandre Burrows was given a major penalty and game misconduct for a hit on Predators forward Paul Gaustad.
"We had a lot of guys selling out," Bonino said. "Especially after you've given up two (power-play) goals, to be able to get that kill and take it into an overtime and kill a 4-on-3, it was really big."
Canucks defenseman Kevin Bieksa, one of their best penalty killers, was given a 10-minute misconduct at the same time Burrows was ejected. Gaustad left the game after the hit from and did not return.
"I felt like we collided more than anything, but you never want to see someone go down," Burrows said. "I've been on the wrong side sometimes and you never want to see someone be down so hope he's alright. That was a big win by the boys. The boys battled hard tonight and found a way to kill that major."
Predators forward Mike Fisher tied the game 4-4 at 14:57 of the third period on a power play. Bonino tried to clear the puck out of the defensive zone, but it bounced off of Fisher and past Canucks goaltender Eddie Lack for Fisher's 19th goal.
Chris Higgins gave the Canucks a 4-3 lead at 5:48 of the third period on a one-timer off of a pass from Burrows. Higgins drove through the middle of the ice and redirected a feed past Predators goaltender Pekka Rinne for a power-play goal. It was Higgins' 12th goal of the season.
"It's hard to keep emotions in check, especially when you don't think some calls are going your way," Higgins said. "You get two guys thrown out on one play. I don't think I've ever seen that before. It certainly is difficult this time of year too, we need the two points. You try to remind yourself with everything going on that we need the win."
Burrows tied the game 3-3 at 1:23 of the third period on a shorthanded breakaway. Burrows hesitated, then put it past Rinne for his 16th goal.
Cody Franson opened the scoring on a power play 4:30 into the game on a wrist shot from the point. Forward Colin Wilson drove to the net and Franson shot the puck past Lack for his seventh goal of the season and first since being acquired from the Toronto Maple Leafs.
"I think he's done well," Predators coach Peter Laviolette said. "He has a real good shot that he can get off quick. It's hard and finds the net and finds a way through. The power play had close to 20 shots on net and probably 30 attempts. There were so many good looks that I would've liked to have seen more."
Taylor Beck doubled Nashville's lead at 8:15 of the first period on a breakaway. Beck took a pass from Gaustad and sent a wrist shot that trickled through Lack's pads for his eighth goal.
Vancouver forward Lindey Vey scored to make it 2-1 at 4:04 of the second period on a wrist shot that beat Rinne through the five-hole. Vey skated into the Predators zone and his shot got around two defensemen for his 10th goal.
Canucks forward Jannik Hansen tied the game at 6:04 of the second on a slap shot that beat Rinne on the blocker side. Hansen used Predators defenseman Roman Josi as a screen and scored his 15th goal to make it 2-2.
Viktor Stalberg gave the Predators a one-goal lead with 29.4 seconds remaining in the second period on a wrist shot that beat Lack. Stalberg took a pass from defenseman Anton Volchenkov and shot from the right faceoff circle for his second goal.
"They have a great home record," Desjardins said of the Predators (28-8-3). "They're one of the top teams in the League. For us to come in after playing (Monday) night and getting behind, it just shows a lot of character in our team."
Predators defenseman Shea Weber missed his third consecutive game because of a lower-body injury and is day-to-day.