It was the sixth road win in a row for the Islanders, who forced the overtime when Brock Nelson's goal early in the third period evened the score.
Brian Strait helped set up the winner with a pass to Grabner in the Avalanche zone. Grabner skated across the slot before circling back and firing from between the circles to get the puck past Semyon Varlamov.
Kevin Poulin, who had 30 saves, won his fourth straight decision and improved to 5-1 in his last six games.
That's a really tough thing to play through; when you finally are thrown out there, the game is fast, intense, every single play matters, you've got to find a way to play through that and make smart plays. So it's a huge testament to [Vermette] and some other individuals in our locker room that are putting their own ego, their own wants and needs aside, and are ready for those opportunities when they do come.
— Blackhawks captain Jonathan Toews on teammate Antoine Vermette, who returned from being a healthy scratch in Game 3 to score the double-overtime winner in Game 4