Patrick Marleau netted two power-play goals in 1, at HP Pavilion.
Kyle Brodziak scored the lone goal for Minnesota, which had its five-game win streak snapped.
Niklas Backstrom made 33 saves in a losing effort.
Marleau's first goal came just 2:34 into the second period when Backstrom stopped a Dan Boyle shot from center ice, but the rebound was not gathered by the goaltender or Wild defenseman Justin Falk as it sat to the left of the goal and Marleau shot the loose puck into the net.
The forward added his second goal of the period when he ripped a one-timer from the right circle that screamed past Backstrom's glove at the 15:34 mark.
Mitchell's tally came with less than two minutes left in the stanza when Michal Handzus won an offensive zone faceoff back to Mitchell and his one- timer found the twine.
Brodziak's quick shot from the slot into the top-left corner with 6:27 left in regulation ended Niemi's shutout bid.
San Jose improved to 3-0-1 on a six-game homestand...The Sharks have won 16 of the last 20 meetings with Minnesota...The Wild are 1-8-1 in their last 10 games in San Jose.