Elias Pettersson scored his fourth goal in five games, Danton Heinen had two assists and Kevin Lankinen made 16 saves against his former team for Canucks (9-5-3), who were coming off a 4-1 win against the Chicago Blackhawks on Saturday.
Vancouver is 3-4-3 at home this season and has allowed at least five goals in five of those 10 games.
“We really pride ourselves on our play without the puck,” Canucks coach Rick Tocchet said. “It seems on the road (6-1-0) we're a little bit better. ... Too many goals at home.”
Center J.T. Miller only played two shifts in the third period and finished with 11:41 of ice time, his lowest in six seasons in Vancouver.
“He wasn't one of the guys I thought could get us back in the game,” Tocchet said.
L’Heureux gave Nashville a 1-0 lead at 5:28 of the first period. Cole Smith whiffed on a spinning backhand shot in the slot, but the puck went right to L’Heureux, who shot into an open net at the right of the crease.
“Unreal,” said the 21-year-old, who was playing in his 14th NHL game. “Been working a long way and been close to a month now I've been here and hasn't come, so obviously happy to get it out of the way and keep going.”