The winning goal came as the Red Wings got caught on a shift change. Joe Thornton had space on the right side after collecting the puck at the Detroit blue line, skating down the wing and faking a shot to freeze Red Wings goalie Jimmy Howard.
But instead he passed into the slot where Marleau was all alone, one-timing a shot into the open net 7:07 into overtime to give San Jose a commanding advantage over the defending Western Conference champs.
Logan Couture found the net in the third period to forge a tie and Evgeni Nabokov made 32 saves in the victory.
Detroit got goals from Tomas Holmstrom, Henrik Zetterberg and Dan Cleary in a losing cause.
San Jose will attempt to sweep the Red Wings in Thursday's Game 4 at Detroit.