Mitchell Marner scored twice for the Maple Leafs (13-6-1), who were beginning a four-game road trip and have won six of seven.
"It's always fun coming into a new arena and kind of just seeing what's been done to it, kind of just the new aspects of it and the new kind of feeling," Marner said. "It's always fun coming into a new building and it's a pretty good rivalry with this team, just from the fan base and what's been going on, so it's always going to be a pretty loud building coming in here and pretty electric atmosphere.
"I thought we did a good job of coming in and going at them right away and kind of putting our game down first."
Ilya Sorokin made 37 saves for the Islanders (5-8-2), who have lost six straight games in regulation and have been shut out twice in the past five.
New York, which lost its second straight at the new arena, again played without forwards Josh Bailey and Anders Lee, and defensemen Adam Pelech and Andy Greene, who are in NHL COVID-19 protocol.
"Put it this way, it hasn't been easy," Islanders coach Barry Trotz said. "We're not looking for excuses, we get it. We're just trying to win a hockey game. Last night (a 5-2 loss to the Calgary Flames), we played well enough to get a point at least; tonight, we didn't play quite as well."
Marner scored on a shorthanded breakaway at 3:31 of the first period during a 4-on-3 kill to give Toronto a 1-0 lead.
New York was 0-for-3 on the power play.
"A lot of times it's execution and effort," Trotz said. "If one of those two things are failing, then you get bad results."