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.
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.
Luongo was tested early, as he turned aside 13 Nashville shots in the opening period.
The Canucks' defense held the Predators to just five shots each in the second and third periods.
The shutout was Luongo's second of the season and 62nd of his career. His 35 shutouts with the Canucks are a franchise record.
Nashville had a late power play after Alex Burrows was sent off for slashing at 17:47 of the third, but they 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.
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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. Bieksa did not appear to be involved in any major collisions during the game.
Bieksa is tied for the Canucks team lead with five goals.
NOTES: 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.
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