Tomas Hertl, Joonas Donskoi and Joel Ward also scored to help the Sharks extend their season-high point streak to eight games. San Jose has used its longest point streak since going 7-0-1 in March 2014 to move into second place in the Pacific Division.
Martin Jones made 25 saves.
Chris Porter, Charlie Coyle and Jarret Stoll scored for the Wild, who have lost six of their past seven games. Darcy Kuemper made 29 saves but could not stop Pavelski’s game-winner.
Joe Thornton won a faceoff in the offensive zone to Pavelski, who beat Kuemper with a wrist shot for his 23rd goal of the season. Pavelski added two assists on the day.
Stoll had tied the game midway through the third when he knocked a rebound on Jonas Brodin's shot past Jones for his second goal in the past three games.
The Sharks had scored twice in the second period for a 3-2 lead. The first came on the power play when Ward sent a cross-ice pass to Donskoi, who beat Kuemper with a one-timer as San Jose's second power-play unit came through again.
Just 1:38 later, Donskoi missed the net on a chance in transition but the puck came off the back boards to Logan Couture, who tipped it to Ward, who knocked it in with a backhand for his 14th goal of the season.
The Wild fell behind in the opening minutes when Hertl banked a wraparound attempt off Kuemper and into the net. But Minnesota rallied with two goals in the second half of the period.
Porter tied the game when Marco Scandella's point shot hit him in the skate. Porter then kicked the puck to his stick and knocked it into the net for his third goal of the season.
Coyle gave the Wild the lead on the power play when he poked at a loose puck after Jared Spurgeon's point shot hit the cross bar. Minnesota has power-play goals in two straight games after failing to convert on 25 straight chances with the man advantage.
NOTES: Minnesota F Jason Pominville played in his 800th career game. ... Former Sharks D Gary Suter dropped the ceremonial first puck with his nephew, Minnesota D Ryan Suter, taking the draw. ... Thornton had two assists to give him 930 in his career, moving past Larry Murphy for 16th place on the NHL career list. Thornton has 22 points in his past 17 games.