Goligoski also extended his streak of games in which he's at least one point to five. He has seven points over that stretch. The Coyotes have won three of their last four games and have consecutive wins for just the second time since Nov. 18.
Arizona upset a Sharks team scrambling to make the playoffs and in desperate need of a win. San Jose lost for the third time in five games.
The Sharks, coming off consecutive come-from-behind wins against Edmonton and Anaheim, were looking for a season sweep of Arizona.
San Jose had its chances. The Sharks outshot Arizona 41-28 and were 0 for 5 on power plays.
Goligoski scored his eighth goal on a power play that broke a 1-1 tie at 9:35 of the second period. He fired a slap shot from behind the penalty circle past Sharks goalie Martin Jones, 23 seconds after Logan Couture was called for holding.
The Coyotes took an early lead at 7:58 of the first on Kevin Connauton fifth goal. With a collision in front of the goal, Connauton drove the puck past Jones.
San Jose tied it shortly afterwards as Mikkel Boeddeker redirected a Justin Braun slapshot from inside the blue line at 9:20 of the first. With his back to the goal, Boeddeker elevated the puck high into the net past Wedgewood's right shoulder for his eighth goal.
Coyotes: Coyotes goalie Scott Wedgewood left the game early in the third period after a collision with Timo Meier. Antti Raanta, the regular starter on an off day off after a 37-save game in Monday's 6-1 victory over the Chicago Blackhawks, finished the game for Arizona. Wedgewood had 29 saves and Raanta had 12.
Sharks: Jannik Hansen was promoted from the fourth to third line, swapping roles with Melker Karlsson. . D Tim Heed and F Brandon Mashinter were called up from the AHL San Jose Barracudas. F Tomas Hertl left the game in the first quarter after crashing into the boards on a short-handed scoring chance.
Coyotes: Open a seven-game homestand on Thursday against Montreal.
Sharks: Play at Vancouver on Thursday.