Couture took a cross-ice pass from Kevin Labanc and fired a wrist shot from the dot in the left circle past the blocker of Marc-Andre Fleury, evening the best-of-seven series at a game apiece.
Brent Burns also scored two goals, the third multi-goal playoff game of his career, and Joe Pavelski added two assists for the Sharks. Martin Jones, pulled after allowing five goals on 13 shots in the opening loss, bounced back to stop 26 shots to win for the fifth time in six playoff games this season for San Jose.
William Karlsson scored two goals and Nate Schmidt also scored for Vegas, which suffered its first-ever playoff defeat. Marc-Andre Fleury had 43 saves for the Golden Knights.
Vegas, which scored four goals in 12 minutes of a 7-0 win in Game 1 on Thursday, managed just five shots in the first period but still led 1-0 on a rebound goal by Karlsson.
Cody Miller fired a shot from the right point that bounced off the boards to Karlsson to the left side of the net, where he slapped a bad angle shot in off the pads of Jones for his second goal of the playoffs.
Karlsson scored his second goal just 26 seconds into the second period, beating Jones on the glove side with a wrist shot just inside the left circle. But the Sharks cut it to 2-1 just 94 seconds later on a power play goal by Burns, whose shot from the right point deflected off the arm of Vegas center Pierre-Edouard Bellemare and past Fleury, snapping a shutout streak of 144 minutes and four seconds for the Golden Knights' goalie.
San Jose tied it, 2-2, midway through the period following a bad clearing pass by Fleury. Tomas Hertl grabbed the puck and circled behind the Vegas net and then fed an open Couture in the slot when he fired a shot over Fleury's glove.
Burns then gave the Sharks their first lead of the series four minutes later when he got a faceoff from Pavelski at the right point, then skated in and around the net and beat a diving Fleury with a wraparound.
The Golden Knights tied it at 13:28 of the third period when Schmidt's one-timer from the high slot deflected off the skate of a sliding Melker Karlsson and under the glove of Jones.
Vegas then appeared to win it at 16:58 of the first overtime when Jonathan Marchessault backhanded in a shot from the slot. However, the goal was overturned on video review for goaltender interference when it was ruled Marchessault had run into Jones and his stick while skating by the crease just before taking his shot.
Game 3 of the series is Monday night at SAP Center in San Jose.
--Field Level Media
San Jose | Vegas | |
Brent Burns 3 | Points | William Karlsson 2 |
Brent Burns 2 | Goals | William Karlsson 2 |
Joe Pavelski 2 | Assists | Nate Schmidt 1 |
Brent Burns 1 | Power Play Goals | N/A |
N/A | Short Handed Goals | N/A |
Martin Jones .897 | Save Percentage | Marc-Andre Fleury .915 |
Martin Jones 26 | Saves | Marc-Andre Fleury 43 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
San Jose | 47 | 4 | 2-7 | 2-2 | 12 | 49 |
Vegas | 29 | 3 | 0-2 | 5-7 | 22 | 40 |