Said Marchessault: "He is in his crease, but I'm not even in his crease too. I'm going through and working for position in front of the net, and the puck hits me. He doesn't even make the save. I guess it's a tough one."
Golden Knights defenseman Nate Schmidt tied the game 3-3 at 13:28 of the third period with a low one-timer from the point that handcuffed Jones.
The Sharks scored three straight goals in 12:07 during the second period after falling behind 2-0.
Burns scored a power-play goal with a slap shot that deflected off Vegas forward Pierre-Edouard Bellemare to get San Jose to within 2-1 two minutes into the period, ending Fleury's shutout streak at 143:51.
The Golden Knights, who won their first five playoff games, had not allowed a goal since Los Angeles Kings center Anze Kopitar scored at 17:56 of the third period in a 3-2 Vegas victory in Game 3 of the first round.
Fleury (43 saves) was putting the loss in the past before walking out of the dressing room.
"I think I have lost every way possible," he said. "It doesn't matter if you lose 1-0 or in the second overtime. A loss is a loss, and you have to move on."
Couture tied it 2-2 at 11:08 when he snapped a high one-timer past Fleury, who had a chance to freeze the puck before the goal but elected to play it. Burns gave the Sharks a 3-2 lead when he scored at 14:07, circling the net and beating Fleury with a wraparound for his second goal of the night.
Vegas coach Gerard Gallant challenged for goalie interference by Meier, but the Situation Room upheld the goal, ruling Golden Knights defenseman Colin Miller caused Meier to contact Fleury.
William Karlsson scored the first of his two goals on a sharp-angled shot with 2:01 left in the first period to give Vegas a 1-0 lead. He scored again 26 seconds into the second to make it 2-0, snapping a shot from the right circle past Jones.
San Jose was 2-for-7 on the power play after going 0-for-5 in Game 1.
"If you give them chances [on the power play], they are going to bury one," Vegas forward James Neal said. "That is what happened."