WATCH: All Islanders vs. Sharks highlights
"It was just get right back out there and go after it," Marleau said. "You don't like to see another team tying it up that late in the game, but I think we had the right mindset going right back out there and trying to get the win right away."
Joe Pavelski and Burns scored in the second period for the Sharks (12-8-1), and backup goaltender Aaron Dell made 26 saves. The Sharks have won the first three games of their five-game homestand.
Anders Lee scored in the first period for the Islanders (6-10-4), who are 1-6-1 on the road.
"I can't fault the guys," Islanders coach Jack Capuano said. "I can't fault the way they're playing, the compete level, desperation in our game, the structure that we're playing with. To come into this building and the effort that we had and the chances we had and the limited chances that we gave them. It was a good hockey game. It should've gone into overtime. We just didn't get the bounce."
Dell defeated the Islanders for the second time this season in his third NHL start. He made his NHL debut on Oct. 18 against New York at Barclays Center and made 21 saves in a 3-2 win.
"You get to know their tendencies a little bit," Dell said. "You get to know their top guys, and I think it helped a little bit to have some experience against them."