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.
I have been blessed to play for 16 years in the NHL; it has been an amazing ride. I would like to thank the Tampa Bay Lightning and New York Rangers organizations and owners for providing me the opportunity to play the sport I love for so many years. I could have never played for so long or accomplished all that I have without the unwavering love and support from my wife, Heather, our three sons, Ryan, Lucas, and Mason, and my parents.
— Martin St. Louis after announcing his retirement from the NHL on Thursday