John Tavares, Blake Comeau, Milan Jurcina and Ty Wishart also scored for an Islanders team that won its third straight and showed it still had some offensive punch left after a brawl-filled 9-3 win over the Pittsburgh Penguins on Friday.
Kyle Okposo had four assists for the Islanders, who rallied from a 4-2 second-period deficit.
Okposo set up the winning goal, hitting Grabner on the fly at the Sabres' blue line. With a step on defender Andrej Sekera, Grabner snapped a shot beating Ryan Miller just inside the left post.
Drew Stafford scored three times for the Sabres, who had a season-best three-game win streak snapped. For Stafford, it was his league-leading fourth three-goal game of the season and second in three outings. Tyler Ennis had three assists, while Jochen Hecht, Tyler Myers and Nathan Gerbe also scored for Buffalo.
Miller struggled, allowing seven goals on just 26 shots.
The Islanders had goaltending troubles of their own as starter Mikko Koskinen was chased after allowing four goals on 14 shots. Al Montoya earned the win, stopping 12 shots in his first NHL appearance since April 2009.
The Islanders won a day after the NHL suspended Trevor Gillies (nine games) and Matt Martin (four), and fined the team $100,000 for failing to control its players against the Penguins in a game that produced 346 penalty minutes, 10 ejections, 15 fighting majors and 20 misconducts.
Injuries have also decimated the Islanders' lineup as they remain down numerous regulars, including starting goalie Rick DiPietro (broken bones in face), Doug Weight (back) and Mark Streit (shoulder). Comeau, meanwhile, returned after missing four games with a concussion.
Through all that adversity, the Isles proved feisty in a back-and-forth game that featured three lead changes, and had the Sabres forced to rally back after they led 4-2 on Gerbe's goal that chased Koskinen 4:31 into the second period.
New York rallied back, and won for only the second time this season (2-20-2) when trailing after 40 minutes.
Trailing 5-4, the Islanders capitalized on a 5-on-3 advantage to take the lead on a pair of power-play goals scored 1:16 apart.
Jurcina one-timed a shot from the left circle to tie it at 5, and then Wishart had his wrister from the point deflect off a crowd in front and dribble in past Miller, who whiffed in his attempt to glove the puck with 7:12 remaining.
Stafford responded by scoring 31 seconds later, converting a rebound in off the right post after Montoya was left out of position after stopping Jordan Leopold's point shot.
Notes: Grabner opened the scoring 40 seconds in. It was New York's fastest to start a game this season, and fastest since Tim Jackman scored 16 seconds in during a 5-4 shootout loss at Florida on Nov. 14, 2009. ... Grabner extended his point streak to five games (nine goals, two assists), while . ... Sabres RW Patrick Kaleta returned after missing six games with a left hand injury.