Nik Antropov, Dominic Moore, Ian White and Pavel Kubina each scored for the Maple Leafs, who were coming off a home-and-home sweep of the New York Rangers. Jason Blake and Mikhail Grabovski both collected two assists, while Vesa Toskala finished with 40 saves.
Sean Bergenheim, Jon Sim, Dean McAmmond and Mark Streit found the net for the Islanders, who have lost nine of their last 11 games. Joey MacDonald made 29 stops for New York, which rallied from a two-goal deficit late in the third period.
Streit faked a shot and slid the puck between Toskala's pads to make it 4-3 with 8:31 remaining. The Toronto netminder then had Sim's high wrister skip off top of his catching glove, tying the contest with 3:07 to play.
The game went to overtime, the fifth straight contest Toronto has played beyond regulation (3-0-2), and ultimately was decided in a shootout.
New York's Frans Nielsen was the first participant in the extra segment and his bid caught iron. After MacDonald turned away Nikolai Kulemin, Jeff Tambellini beat Toskala with a sizzling wrister from the high slot and Blake scored off a nifty spin-o-rama.
Toskala then used the poke check to deny Kyle Okposo, and Stapleton fired a low shot that rang off the near post to cement the win.
White gave the visitors an early 1-0 lead as his quick shot from the top of the left circle eluded a screened MacDonald 1:27 into contest.
Moore widen the advantage with a short-handed tally, taking a drop pass from Blake and beating MacDonald on the glove side 57 seconds into the middle stanza.
A missed opportunity on a penalty shot kept the Isles staring at a two-goal deficit. With Toronto enjoying the man advantage, White coughed the puck up to Bergenheim just inside the blueline, allowing the Finnish left winger to break in alone on Toskala. Bergenheim dashed down the ice and was harassed from behind by Maple Leafs defenseman Anton Stralman, resulting in the one-on- one showdown with his fellow countryman that was won by Toskala, who denied Bergenheim with the left pad.
McAmmond put the home team on the board with 5:28 remaining in the second period. Bill Guerin's feed from behind the enemy cage found McAmmond, whose rising shot from the left faceoff dot beat Toskala with help from a screen in front by Sim.
At 2:21 of the third period, Isles backliner Brendan Witt caught Niklas Hagman with the left elbow and assessed a five-minute major, but a blunder in the neutral zone led to a short-handed tally.
Grabovski made a poor decision with the puck and it ended up on the stick of Bergenheim, who had a clear path to the net and, this time, solved Toskala, using the backhand to lift the disc past the goalie's glove at 3:30.
Still on the power play, Kubina put Toronto back on top two minutes later with a drive from the point that went off the right shoulder of MacDonald and dribbled across the goal line.
Antropov made it 4-2 at 7:05.