Brad Richardson, Mike Santorelli and Zack Kassian also scored for the Canucks, who had lost all five regular season meetings between the teams the past two seasons and were swept by San Jose in the first round of the playoffs last spring.
Joe Thornton and Mike Brown scored for the Sharks, who lost their fourth straight game, but just the second in regulation all season.
Antti Niemi allowed four goals on 12 shots before being replaced early in the second period as the Canucks controlled the play for much of the first 40 minutes and weathered a strong push from San Jose in the third.
Vancouver killed an early power play and got a strong save from Luongo on a tip by Logan Couture in the first half of the period to help seal the victory.
Vancouver got the win without any production from their top line of the Sedin twins and Ryan Kesler.
Henrik Sedin had points in an NHL-best 12 straight games, while brother Daniel had his seven-game point streak snapped. Kesler had 10 points in the past nine games before being held off the score sheet.
The Canucks dominated the second period, outshooting the Sharks 17-5 and getting the only goal when Kevin Bieksa's point shot hit Kassian's skate and went past Niemi to make it 4-2 with 14:38 left in the second.
That ended Niemi's night after he allowed four goals for the third time in four games.
Alex Stalock came in and stopped all 22 shots he faced but the Sharks were unable to get anything past Luongo the rest of the way and lost.
It was a wide-open first period with odd bounces and costly misplays leading to five goals as the Canucks took a 3-2 lead.
The Sharks got the first break when Thornton innocently played the puck around the boards only to have the puck hop back over the net and deflect off Luongo's shoulder before falling into the net for a goal just 1:17 into the game.
But the Canucks answered quickly when Bieksa took the puck away from Tyler Kennedy along the boards and Richardson capitalized by shooting it past Niemi.
After Santorelli and Brown traded goals on nice plays in transition, another San Jose turnover helped the Canucks take the lead into the second.
Jason Demers and Scott Hannan misplayed a puck in their own zone and Higgins got it and flipped it over to make it 3-2 with 1:05 to play in the first.
NOTES: Vancouver's Ryan Stanton fought Andrew Desjardins in the first period after the Sharks forward gave Luongo a snow shower after the whistle. ... After having at least 50 shots the past two games, the Sharks were held to 11 in the first two periods. ... The Canucks have killed off all 14 power play chances by the Sharks this season.