With 1:47 left and the Sharks with the extra attacker after pulling goaltender Evgeni Nabokov, Turco made a glove save on a close-in shot by Joe Pavekski to preserve his second shutout of the season.
Turco was called for a tripping penalty when he used his stick to take down San Jose's Steve Bernier in front of the net with 47 seconds left, but the Sharks were unable to score on the ensuing power play.
Turco also had a pad save on a shot by Jonathan Cheechoo that seemed ticketed for the lower right corner of the net with 6:38 remaining. Officials checked the save on replay, ruling that the puck stayed under Turco's pad and never crossed the goal line.
Turco came up with a tough stick save on Patrick Marleau with 11 minutes left, and made a sliding stop on Marleau's point-blank attempt with 9:20 left to preserve his second shutout of the season.
The Stars finished the game minus six injured regulars, including Modano, who exited for the locker room in the second period with an unspecified lower body injury and did not return.
Also out for Dallas were left-wing Brenden Morrow (groin), forward Eric Lindros (bruised foot), defencemen Trevor Daley (concussion) and Darryl Sydor (arm) and right-wing Antti Miettinen (lower body).
Nabokov made 12 saves for the Sharks, who wrapped up a 3-1 road trip.
Modano capitalized on the game's first power play with a one-timer from the right circle at 7:46 of the opening period.
The goal was Modano's 10th of the season and 495th of his career.
San Jose turned up the pressure in the second period with a 13-4 shots advantage, but the Sharks were unable to cash in on three power plays.
Notes: The Sharks had won 11 of their previous 13. ...The Sharks were shut out for the second time this season. ... Dallas C Joel Lundqvist made his NHL debut. He was called up Monday from Iowa of the American League because of the Stars' injuries. ... Lindros, who missed his first game of the season, is day-to-day. ... The Stars improved to 8-1-0 against the Pacific Division.