With Buffalo down 3-0 early in the third period, Deslauriers' wrister from the slot sailed through three Islanders before beating goalie Kevin Poulin.
''I heard it hit the post,'' Deslauriers said. ''But I saw (Drew) Stafford and (Brian) Flynn putting their hands up, so I put mine up.''
The goal was the first of three third-period goals in just over 5 minutes for Buffalo, and Tyler Ennis scored in a shootout to give the Sabres a 4-3 victory and snap a four-game skid.
It was Deslauriers' fourth goal of the season, and his second in two games. He also added an assist on Zemgus Girgensons' short-handed goal.
''I'm just putting the puck on net and getting lucky odd bounces,'' Deslauriers said. ''I'm not a guy who looks at my stats like that. It's more about finishing my hits and if I get a chance to bury one, I'll do my best.''
''I thought their goalie obviously elevated,'' Islanders coach Jack Capuano said. ''I mean he was good tonight, but he made some big saves when he had to and that's what you need to do when you win hockey games.''
Poulin was recalled from Bridgeport of the American Hockey League on Tuesday after Jaroslav Halak sustained a lower-body injury.
''I thought he gave us a chance to win,'' Capuano said about Poulin.
Buffalo overcame a 3-0, third-period deficit for just the second time in franchise history, and posted its first three-goal comeback since a 6-5 overtime win against Toronto on April 3, 2012.
The Islanders scored on their second shot of the game when Leddy's slap shot from the left point beat a partially-screened Enroth.
Tavares made it 2-0 at the 11:56 mark with his 14th of the season. The New York captain stole the puck at the left circle and caught Enroth deep in the goal with a high backhand flip.
Tavares added his 15th on a cross-crease pass from Josh Bailey at 15:05.
Poulin made a right pad save on Cody Hodgson's open one-time shot from the slot a minute later to keep the score 3-0.
Patrick Kaleta took a diving shot about 5 minutes into the third period, but Poulin was able to push it wide with his blocker.
That's when things starting clicking for Buffalo.
''A couple guys just turned it up a little bit more,'' Sabres head coach Ted Nolan said. ''Girgensons went to the next level, and can't forget about Stewart.''
Deslauriers ruined Poulin's shutout bid with his shot through traffic with 6:39 gone in the third.
Then, with Stafford in the penalty box on a goaltender-interference call, Girgensons scored his 10th of the season to make it 3-2.
The Buffalo center took a long pass from Deslauriers and held off Johnny Boychuk with his backside before wristing a shot past Poulin for a short-handed goal at 10:01.
''After the second we told ourselves in the locker room it was time to step up, pick it up and come back in the third,'' Girgensons said.
Stewart picked up a pass from Stafford 1:51 later, slipping the puck between Poulin's legs to tie it a 3. The fans reaction after his goal was ''for sure'' the loudest Stewart's heard them.
''They were fired up,'' he said. ''As soon as we got that short-handed goal they were really fired up in the building and they really gave us a boost tonight.''
NOTES: Halak was placed on injured reserve, retroactive to Dec. 20. ... Sabres D Rasmus Ristolainen left the game with an illness just a minute into the second period. ... Grigorenko was recalled from Rochester before the game.