Owen Nolan, returning from a 10-game absence caused by a leg injury, produced a Minnesota goal in helping the Wild slow down the top team in the Western Conference.
San Jose had won three of its previous four games.
Devin Setoguchi and Milan Michalek scored for the Sharks and Evegni Nabokov stopped 29 shots.
San Jose tied the game with 23.6 seconds left in regulation on a goal by Backstrom after Nabokov had been pulled for the extra attacker.
The Sharks had won eight straight in the series.