The Canucks have won consecutive games on their four-game road trip after losing three straight.
Nashville has lost three of its past four.
With the game still scoreless in the third period, Maxim Lapierre had the puck behind the Nashville goal line and carried it up to the right circle.
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He then spun and sent a shot toward Predators goaltender Pekka Rinne. Rinne kicked the puck away with his right pad, but Weise was there to put away the rebound for his first goal of the season.
"I've been frustrated with myself for not having contributed offensively like I would like, but I think our line has been playing well," Weise said. "We've been getting chances, and it is really good to get that one."
Weise's previous goal came nearly a year ago, also in Nashville. Three of his five career goals have been scored against the Predators.
Luongo was tested early, as he turned aside 13 Nashville shots in the opening period.
"The first period, we were looking to find a little bit of energy and I think we built off that really solid performance from Louie in the first period," Canucks coach Alain Vigneault said. "He permitted us to find our legs, find our execution, find our energy, and we were much better in the second and the third."
The Canucks' defense held the Predators to just five shots each in the second and third periods.
"They came out strong, but we were able to weather the storm," Luongo said. "The last two periods, I thought we played basically the type of hockey we want to play, especially playing against these guys."
The shutout was Luongo's second of the season and 62nd of his career. His 35 shutouts with the Canucks are a franchise record.
"In the end, when we got down and we got a little desperate, we played pretty well, but other than that, we weren't very good tonight," Nashville captain Shea Weber said.
Nashville had a late power play after Alex Burrows was sent off for slashing at 17:47 of the third, but the Predators failed to record a shot on goal during the man-advantage even with Rinne pulled for an extra attacker for the final 1:15 of the period.
"We got scored on and then we started to kick it into another gear," Nashville coach Barry Trotz said. "You need to kick it for 60 minutes and we didn't get it done."
Canucks defenseman Kevin Bieksa left the game with what the team called a lower-body injury and he did not return.
After playing 7:20 of the first period, Bieksa took just two shifts in the second before going back to the Vancouver locker room.
Following the game, Vigneault said that Bieksa "tweaked a groin a little bit," and that the team would know more about his condition Saturday."
Bieksa is tied for the Canucks team lead with five goals.
- This game marked the fourth time this season that the Predators have gone into the third period with the score tied 0-0.
- After playing the past 10 games, Nashville D Jonathon Blum was a healthy scratch Friday night.
- Vancouver did not score a power-play goal in the game. The Canucks had at least one power-play score in their past three games.