"I'm pretty pleased that we got five out of six points this past week," Reimer said. "It's nice to get some results."
"Christmas is miserable any time you lose," Toronto coach Ron Wilson said. "We found a way to win."
Toronto wasted little time getting on the board as MacArthur headed to the right crease and knocked a loose puck past Nabokov just 1:43 into the game.
Kadri scored near the end of a Toronto power play to double the lead at 4:22.
The Maple Leafs pushed it to 3-0 with 8:45 to go in the first when Gunnarsson beat Nabokov with a slap shot from the center point for his first goal of the season.
"We came out strong," Reimer said. "They may have had some holiday distractions, but I feel we were just more determined."
New York finally broke through with 4:15 to go as Okposo came in on a break and beat Reimer to the glove side with a wrist shot. Nielsen connected on a power-play rebound 40 seconds into the second period to trim the deficit to 3-2.
Crabb put the Leafs back up by two with his sixth goal of the season, which came on a 2-on-1 short-handed break.
The Islanders pulled back within one when Tavares buried a rebound with 9:10 to go in the game.
Lupul closed the scoring on an empty-netter with 8.9 seconds left.
"We were a little sluggish," Tavares said. "We battled back, but we made too many mistakes and dug ourselves too deep a hole early."
The Maple Leafs opened a four-game road trip. After the New Year, Toronto plays nine of ten at home. ... Islanders F Matt Martin threw a check about halfway through the game and went down. He was taken to the dressing room.