The win gives Vancouver a 3-1 lead in the best of seven series which shifts back to Vancouver for an elimination game on Saturday.
With the scores tied at 2-2 in the third period, Ryan Kesler burst through the Predators defense and beat Nashville goalie Pekka Rinne for a spectacular powerplay goal at 07:28 to give Vancouver a lead they would not lose.
"That was an unbelievable goal," defenseman Christian Ehrhoff said of his team-mate's effort.
"A nice goal and at a great time. He's worked really hard all playoffs long, and he got another game-winner. Well-deserved."
Canucks center Henrik Sedin then scored his first goal of the play-offs into an empty net with 21 seconds remaining to make the game safe.
Rinne made 24 stops for Nashville to keep the Predators within striking distance until the end despite the Canucks dominating play for long periods.
Although not as busy as his counterpart, Roberto Luongo (19 saves) had to make several difficult stops particularly during a five-on-three man advantage for Nashville in the second period.
"They were in striking distance and we got a couple of big plays from our goaltender," Canucks coach Alain Vigneault said.
"We had a great job from Dan Hamhuis, Alex Burrows and Ryan Kesler, who were out there for almost the full five-on-three. They were at the right place, doing the right things."
Vancouver opened the scoring at 15:04 in the first period with a goal by Ehrhoff, but the lead was short lived as Joel Ward levelled on a powerplay in the final minute of the period.
Vancouver regained the lead with the only goal in the second period via the stick of Alexander Edler but Cody Franson scored early in the third period to tie the game before Kesler pounced.
"We've been on death's doorstep a couple times," Nashville coach Barry Trotz said.
"In the Anaheim series, we were there, and we found a way to come back and win," Trotz said of his team's 4-2 series win over the Ducks.
"In Vancouver, we were there, and you know we find ways. And as I said, we've dug ourselves a hole but we've been in a few holes this year and this group has been able to do it all year."