Frans Nielsen, Calvin De Haan and Cal Clutterbuck scored third-period goals to lead the Islanders to the victory.
New York (16-22-7) kicked off a six-game road trip with their second win in two nights with backup Kevin Poulin in goal. Poulin relieved injured starter Evgeni Nabokov on Monday and backstopped the Islanders' 7-3 win over Dallas.
Poulin made 23 saves against the Maple Leafs.
It was another frustrating loss for Toronto (21-18-5), which outshot the Islanders 26-25 in its first game since being beaten 7-1 at home by the New York Rangers on Saturday night.
Kyle Okposo and Michael Grabner also scored for the Islanders, and John Tavares, named to Canada's Olympic team earlier Tuesday, added three assists after registering five points against Dallas.
Tyler Bozak, Mason Raymond and Joffrey Lupul scored for Toronto.