Cody Franson scored in regulation for Nashville and Devin Setoguchi tied it midway through the second period, with an assist from Marleau.
The Predators took seven shots in the third period and the Sharks had 17, but neither team could score.
Franson opened the scoring on a first-period power play at 6:48 with a wrist shot from the center of the right circle that beat San Jose goalie Antti Niemi.
Setoguchi tied the game at 9:13 of the second. He skated down the right side and beat Rinne with a wrister high over his left shoulder from the lower edge of the right circle.
NOTES: Setoguchi has 10 points (five goals, five assists) in his last 10 games. ... Marcel Goc was back in the lineup after missing one game for the Predators. ... Also back for the Predators was Marek Svatos, who had not played since sustaining a knee injury Jan. 13.