It all came in a wild final 3:03, as Grabner got a good carom and snapped in the go-ahead goal at 16:57 of the third and Nabokov got some help from the right post on Thomas Vanek's penalty shot with 1:24 left.
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Nabokov became the 26th goaltender to reach 300 victories. Grabner added an empty-netter with 29.7 seconds left, his first two-goal game of the season. The Islanders broke through in the third after a handful of golden scoring chances, including Grabner hitting the crossbar with 6:42 to play.
"I've had so many chances the last two games," said Grabner, who was stopped on a penalty shot and another breakaway in Thursday's 3-2 loss to the Flyers and had two other good chances turned aside by Sabres goaltender Jhonas Enroth. "After I hit the crossbar, I didn't know what else to do."
As it turned out, the best play he made was stopping in the slot on his next shift. John Tavares, who had two assists to extend his point streak to eight games, sent a pass across the slot and just behind Grabner; Mark Streit sent the puck in front, where three Sabres converged on P.A. Parenteau. The puck squirted right to Grabner with Enroth sliding the opposite direction, and Grabner slammed it home to vent a few games' worth of frustration.
"Grabs works extremely hard every night and he gets his chances," said Jack Capuano, who moved Grabner to the left with Parenteau and Frans Nielsen for the third period. "It's good to see him bury a couple."
A curious call by referee Eric Furlatt nearly buried the Isles' celebration. Streit went to chase the play around the net and appeared to stumble into the goal, lifting it off its moorings with the Sabres circling the net. Furlatt didn't hesitate to call it a deliberate play, meaning a penalty shot since it was in the game's final two minutes.
It stung more because an identical play had happened at the other end with the game 2-2 earlier in the third, when 6-8 Sabres defenseman Joe Finley stumbled into his net as the Isles controlled the play. The officials blew that play dead.
So Nabokov needed to stop Vanek, who snapped a shot through Nabokov's pads, off the post and out.
"I would say that the only spot that was open was the post," Nabokov joked. "It's a big number, for sure."
Even bigger for the Isles was Nabokov making his 11th consecutive start. He had another stickhandling miscue, giving away a routine play behind the net that led to Derek Roy's tying goal at 16:58 of the second, just 42 seconds after Kyle Okposo snapped a 1-1 tie.
But the Islanders finished off a week in which they were the better team in three straight games. "We played extremely well against Philly and didn't get the win," Capuano said. "Tonight, we got our chances and we didn't quit."