Grabner's goal 5:51 into the third period gave the Islanders a 3-2 victory, but this game might be remembered more for its crazy ending.
New Jersey forward Zach Parise had a goal in the final second disallowed because it was ruled he kicked it in – a decision the Devils captain was not happy about.
"It definitely hit my skate, but is that a kicking motion? I definitely don't think it was," Parise said. "Of course I was angry, and then they make the wrong call."
The game-winning goal was a great play by Grabner. He poked the puck away from Kovalchuk as the New Jersey forward tried to carry it out of his own zone with the Devils on the power play. Grabner collected it and snapped a shot past Martin Broduer for his seventh goal of the season.
New York had lost 14 of 16 games, and all seven on the road before Saturday. The Devils had won four of five, including a 1-0 victory Friday against the Islanders on Long Island.
"Our guys battled," Isles coach Jack Capuano said. "They battled the last nine periods. We did get some breaks tonight. It takes a few breaks to win a game. I'm just glad they got the two points."
Matt Moulson put the Islanders in front at 11:28 of the first period. He collected a drop pass from PA Parenteau and snapped a shot from the right circle past Brodeur for his seventh of the season.
Both of New Jersey's goals came from rookies. Defenseman Adam Larsson scored his second of the season to even the score at one 4:20 into the second period. Kovalchuk dropped the puck to Larsson on a 3-on-2 and he fired a wrist shot from the top of the circles past New York goalie Al Montoya.
Josh Bailey put the Islanders back in front less than eight minutes later. Brian Rolston won a battle in the left corner and found Bailey in front at 11:59 of the middle period.
New Jersey forward Adam Henrique leveled the contest at two 3:59 into the third period with his fifth of the season, but Grabner stole the puck from Kovalchuk and scored less than two minutes later.
"It was nice to get the one," said Grabner, who was also on the ice for both of New Jersey's tallies. "I think we created some offense on the PK, but it's just good that we killed off the penalty."
The Islanders won a faceoff in the final seconds to the right of Montoya, but the Devils regained control and when the puck ended up at the feet of the Islanders goaltender Parise was all alone trying to jam it across the line.
He swiped at it twice with his stick, but the puck went off his skate and in – and the official review determined it was a distinct kicking motion.
"I watched the play and I'm not sure I agree with the decision based on my view of the replays," Devils coach Peter DeBoer said. "To me, it wasn't what I would consider a distinct kicking motion."
Material from wire services and team media was used in this report.
1 - 0 NYI
1 - 1 Tie
2 - 1 NYI