Niemi and the Sharks defense were the difference in this one, unlike in the first meeting between the teams, won 9-2 by San Jose on Oct. 8. Niemi, who has 27 NHL shutouts, was particularly strong during a Rangers power play early in the third.
San Jose, tied with Anaheim atop the Pacific Division, is 11-2-1 in its past 14. In a 12-game stretch against Eastern Conference opponents that ends Tuesday at home versus Florida, the Sharks are 9-1-1.
Henrik Lundqvist made 28 saves but was denied in his first attempt to set the Rangers record with his 302nd victory. He equaled Mike Richter's mark Friday at Winnipeg.
New York, which lost for the third time in four games, dropped one point behind Philadelphia in the Metropolitan Division race and into an Eastern Conference wild-card position.
San Jose, which had 11 shots in the first period, did its best offensive work on its second penalty-kill. The Sharks got off four shots while short-handed and took the lead on Couture's solo effort.
Couture took the puck away from Mats Zuccarello in the neutral zone, raced ahead of Rangers forward Brad Richards, shook off harassment from behind, and beat Lundqvist with a backhander at 11:48 for his 19th goal — second short-handed.
The Sharks weren't whistled for any penalties in their win over the Islanders on Friday.
San Jose came out much better at both ends in the second period and held a 10-7 edge in shots during the scoreless frame, though the Rangers thought they tied it with 3:15 left.
During a stoppage, all four officials gathered in front of the scorer's table. A lengthy video review was conducted in Toronto to see if Carl Hagelin's stuff attempt at the left post had nudged the puck over the line.
Numerous replays failed to show the puck behind Niemi, who blocked the view, but one zoomed-in and enhanced picture appeared to show the puck disappear behind the post — drawing a huge cheer from the crowd.
Those yells turned to boos when it was announced there was no conclusive evidence of a goal. Rangers coach Alain Vigneault called over referee Dan O'Halloran for an explanation he didn't really seem to accept.
New York's next best scoring chance came with 4:09 left when defenseman Ryan McDonagh, seemingly with an open right side in front of him, had his shot blocked by the reaching stick of defenseman Marc-Edouard Vlasic.
Niemi was the main reason the Sharks went into the first intermission with the lead. He stopped all 20 shots fired at him.
He made two eye-popping saves against struggling forward Derick Brassard, including a point-blank chance with 40 seconds left that Niemi kicked out with his left pad. It had Brassard staring at the ceiling and shaking his head.
Earlier in the period, Niemi quickly moved over to deny Brassard's backhander at the right post off a rebound of McDonagh's shot from the left point.
Lundqvist was also sharp in the first, making a strong save with his chest against Patrick Marleau, who fired the Sharks' first shot from the slot 5:31 in. New York had the game's first seven shots.
NOTES: The Rangers haven't allowed a power-play goal in eight games, killing 21 penalties. ... When San Jose D Scott Hannan was called for tripping in the first, he got his stick caught in the skate of Rangers forward Rick Nash.