Ryan Clowe and Justin Braun also scored, and goalie Antti Niemi made 23 saves as the Sharks won for the ninth time their last 10 games.
Joel Ward and Shea Weber had goals for Nashville, which has lost six of 11.
San Jose missed several scoring opportunities late in regulation and appeared headed for a shootout before Marleau's 27th goal of the season.
That gave the Sharks their second straight win over the Predators and came three days after their season-high eight-game winning streak ended.
It also was the 143rd victory of coach Todd McLellan's career, leaving him nine shy of the all-time record for an NHL coach in his third season.
San Jose led 1-0 and 2-1, but couldn't put the pesky but slumping Predators away until overtime.
Clowe scored on a power play in the first period without having to use his stick. Jason Demers fired a pass from the endboard that Dany Heatley deflected into Clowe's left skate. The puck ricocheted up and over Nashville goalie Pekka Rinne and into the net. Referees reviewed the goal and it was upheld.
The score came just seconds after Heatley missed from in front of the crease, only San Jose's second shot of the opening period. Rinne finished with 30 saves.
Ward tied it later in the first on a power play when he tapped in his own deflected shot at the 14:22 mark. It's Ward's eighth goal of the season and the fourth of his career in 11 games against San Jose. Martin Erat and Weber had assists.
The Sharks, third in the NHL in power play success, went in having converted one of their previous 12 chances with an advantage.
That drought coincided with the loss of defenseman Dan Boyle, who suffered an upper-body injury against Pittsburgh on Feb. 23. Boyle sat out his fifth straight game Tuesday and it's uncertain when he'll return.
In the meantime, McLellan jumbled his power-play units against Nashville. Demers, who had been filling in for Boyle, was replaced by Ian White on the top line. Forward Devin Setoguchi also moved up from the second unit, exchanging spots with Heatley.
The moves paid off initially.
Braun's score, coming from just inside the blue line near the Sharks bench, gave San Jose a 2-1 lead 4:17 into the second and came after Shane O'Brien was called for hooking.
Nashville tied it again less than two minutes later with another power-play goal. David Legwand took a pass and skated in front of the net then shuffled the puck to Weber, who raced in from the left side and flipped it past Niemi.
San Jose missed several opportunities to score in the third before Marleau's winner in the extra period.