The Canucks were 3-for-3 on the power play, with two goals from the second unit.
"It's important to get contributions from everybody," said Gaudette, who had an assist on Pearson's power-play goal in the first period. "That's when we are playing our best, when everybody is going, when everybody is contributing."
After Pettersson gave Vancouver a two-goal lead, Forsberg scored on the power play at 14:26 to make it 4-3.
Pearson scored his second of the game shorthanded into an empty net with seven seconds left for the 5-3 final.
The Canucks matched their goal total from the previous four games.
"We were getting our chances, and the puck just wasn't going in," Gaudette said of the winless streak. "The only thing you can do is grind through it. They will finally go in like they did tonight."
With Predators defenseman Dante Fabbro in the penalty box after being called for holding Pettersson's stick late in the first period, Pearson put the Canucks ahead 1-0 when he scored on the rush 1:25 into the second, his wrist shot from the left face-off circle ending a 14-game goal drought.
"It's been a long time since the last one, so it's nice to get one," Pearson said.