Devin Setoguchi added an empty-net goal with 2.1 seconds remaining and Antti Niemi got his third shutout of the season. He got help from his defenders, who rescued wild rebounds before the Bruins could capitalize. Niemi hasn't lost in regulation in his last eight starts.
Ryane Clowe and Marc-Edouard Vlasic assisted on both goals for San Jose, which has won seven of its last eight.
Tim Thomas had 16 saves for the Bruins, who had won three straight. The only shot Thomas didn't get to was Couture's backhand early in the first period.
San Jose's 18 shots on goal were a season-low, but enough to keep the Sharks moving up in the Western Conference standings.
The Sharks' defense was sharp all game, holding Boston to 26 shots and scoreless in four power plays. Boston was booed by its own fans on the Bruins' fourth chance with a one-man advantage, failing to get a shot on goal during Joe Thornton's 2-minute tripping penalty midway through the third period.
Couture, a rookie who had missed two straight games with the flu, put the Sharks up 1-0 when he took a pass from Clowe, skated across the slot and slipped a backhand past Thomas low to the stick side. Vlasic also got an assist on the goal, which came with 15 seconds left on a power play after Boston was called for too many men on the ice with 14:23 left in the first.
Niemi stopped eight shots in the first period and gave up some dangerous rebounds on many, but the Bruins couldn't tap any of them into the net. Milan Lucic had the best chance off a slap shot from Zdeno Chara that bounced right to him off the post, but Lucic's shot went across the goal and San Jose still led 1-0.
Notes: The Sharks had an apparent goal taken away because of goaltender interference in the second period. ... The Bruins' previous low for fewest shots allowed was 20 on Oct. 28 in 2-0 win over Toronto. ... The Sharks' fewest shots taken was 19 on Jan. 1 in a 1-0 win at Los Angeles.