The 26-year-old Stapleton was undrafted out of the University of Minnesota-Duluth, and signed with Toronto last June after two seasons with Jokerit of the Finnish SM-liiga.
The Maple Leafs needed him in this one as the teams traded goals in the second round of the shootout, with Jeff Tambellini scoring for the Islanders and Jason Blake answering for the Maple Leafs.
The Islanders tied the game with 3:07 left in regulation when Jon Sim's shot from the right circle appeared to deflect off a Maple Leafs player and over Vesa Toskala's glove.
"It was a great pass from (Mark) Streit," Sim said, "and I let it rip."
Ian White, Dominic Moore, Pavel Kubina and Nik Antropov scored for Toronto, while Toskala stopped 40 shots for his third straight victory. The Maple Leafs have also won three straight in extra time.
Streit, Dean McAmmond and Sean Bergenheim also scored for the Islanders, who are 4-1-3 in the last eight home games. Joey MacDonald saved 29 shots for New York.
"It was an ugly game," Toronto coach Ron Wilson said. He then joked: "I'm growing my hair long so you can't see how gray it is."
Toronto needed just 97 seconds to grab a 1-0 lead. White grabbed a puck along the left boards, moved to the top of the left circle and sent a wrist shot past MacDonald.
"We talked about getting off to a good start," Kubina said, "and we did."
The Maple Leafs did even better in the second period, increasing their lead to 2-0 with 57 seconds gone and on a short-handed goal, no less.
Former Islander Jason Blake led a rush and passed to Moore, who took a shot from above the left circle that got by MacDonald. The short-handed goal was just Toronto's third this season, and first on the road.
The Islanders had a golden opportunity to cut Toronto's lead when Sean Bergenheim was awarded a short-handed penalty shot at 8:23. However, Toskala made a pad save on Bergenheim.
"I just wanted to lift it a little higher, and it didn't go," Bergenheim said.
New York made it 2-1 at 14:33 on McAmmond's first goal with the Islanders as he took Bill Guerin's pass in the left circle and sent a shot by Toskala.
Bergenheim made up for the penalty shot miss by tying the game with a short-handed goal at 3:30 of the final period.
While killing a major for elbowing to Brendan Witt, Bergenheim stole the puck at Toronto's blue line and broke in alone on Toskala, beating him with a backhander.
Kubina restored Toronto's lead on the same power play at 5:35 with a slapshot from the high slot. Antropov made it 4-2 at 7:05 on a close-in shot.
Streit cut the lead to 4-3 at 11:29 when he faked a slapshot from the left circle, took one stride in, and beat Toskala with a wrist shot.
"Other than a slow start, I think our guys gave a pretty solid effort," Islanders coach Scott Gordon said. "Especially considering we had a five-minute major against us, the team battled back from 4-2 and tied it up."
Notes: New York defenceman Radek Martinek was injured with 3:20 remaining, and went to the locker room... Toronto's other visit to Long Island this season, the day after Christmas, resulted in injured Islanders goalie Rick DiPietro's only victory in five starts this season.
1 - 0 TOR
2 - 0 TOR
2 - 1 TOR
2 - 2 Tie
3 - 2 TOR