Mitch Marner and Pierre Engvall also scored as the Maple Leafs finished a six-game road trip at 3-2-1.
''It wasn't our best but certainly but much more progress to our game tonight,'' Maple Leafs captain John Tavares said. ''Obviously grabbed the lead on the road and did a good job playing with it.''
Zach Parise got his second of the season for New York, and Semyon Varlamov made 20 saves. The Islanders lost in regulation at home for the second time in 10 games (7-2-1) after dropping their first seven (0-5-2) at the $1.1 billion UBS Arena.
Engvall helped Toronto regain an advantage when he beat the buzzer with 1 second left in the first period to give the Maple Leafs a 2-1 lead. The 25-year-old forward completed a nifty forehand-backhand maneuver before sliding a puck between Varlamov's legs.
''He's a guy that is extremely fit, great athlete, can really skate and he uses that to his advantage,'' Rielly said of Engvall. ''When he is able to beat people wide, swing low and gain speed he can be really dangerous. Obviously beautiful goal tonight. He has taken a lot of pride in his role and that's important.''
Rielly made it 3-1 when he buried a cross-ice feed from William Nylander at 9:42 of the second period. Islanders forward Austin Czarnik was caught watching the puck and lost defensive positioning on Rielly. Alexander Kerfoot also assisted on the play.
''His IQ on the ice is very high, he can read plays very well and cut plays off,'' Marner said of Rielly. ''He is a guy that is very well-respected on our team and does a lot of great things for us.''
Marner opened the scoring with a short-handed goal 6:35 into the game. Rielly stripped the puck from Mathew Barzal in the defensive zone and sent a fluttering puck down the ice that Marner tracked down before guiding a puck past Varlamov. Toronto's alternate captain also scored down a man in the Maple Leafs' 3-0 win against the Islanders here on Nov. 21.
Parise tied it with 1 minute left in the opening period. Islanders defenseman Scott Mayfield sent a bouncing puck into the offensive zone that eluded Toronto's Timothy Liljgren before Parise roofed a backhand over Mrazek's glove.
''We weren't able to generate enough but I thought we gave them two gifts and they are going to capitalize if you make mistakes,'' Islanders coach Barry Trotz said. ''They are a good hockey team.''
The Islanders honored Hall-of-Fame forward Clark Gillies, who died Friday, with a video tribute and a moment of silence prior to the start of the game. The power forward was one of 16 players to win four straight Stanley Cups and 19 straight playoff series with the Islanders during the dynasty years in the early 1980s. New York also wore a No. 9 decal in the upper right-hand corner of their jersey in remembrance of the former captain.
INSIDE THE NUMBERS
Toronto improved to 8-2-2 in 12 games that have taken place on Saturday this season. ... The Islanders fell to 2-10-2 when surrendering the opening goal. ,,, Toronto is 18-3-1 when scoring first. ... The Maple Leafs also improved to 19-0-1 when leading after two periods. ... New York is now 1-12-2 when trailing after 40 minutes.
Maple Leafs: Host Anaheim on Wednesday night.
Islanders: Host Philadelphia on Tuesday night.
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