Jed Ortmeyer scored the game-winner with 4:13 3.
Jared Spurgeon's blast from the right point was deflected in by Ortmeyer, who recorded his first NHL goal since March 28, 2010 when he played with the Sharks.
Niklas Backstrom made 25 saves for Minnesota, which has won three of four.
Thomas Greiss stopped 22-of-26 shots for San Jose, which stayed two points behind idle Phoenix for first in the Pacific Division.
To make matters worse, head coach Todd McLellan left the game in the second period after taking a stick to the head. McLellan ended up being okay and was alert and responsive in the locker room.