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.
It's something that you don't really envision starting this way, but when you put the work in you don't feel like it's unwarranted. You definitely don't envision it unfolding this way, but you do think you can be successful at this level.
— Senators goalie Andrew Hammond, who defeated the Jets on Wednesday to improve to 6-0-1 since making his first NHL start on Feb. 18