Tim Jackman, Frans Nielsen and Matt Moulson also scored, and Blake Comeau added three assists to help the Islanders win their second straight game.
Nikolai Kulemin's goal in the opening minute marked Toronto's only offense. The Maple Leafs had their season-high winning streak snapped at three.
The Islanders killed all seven Maple Leafs power plays, including four in the final period and scored short-handed for the second consecutive game.
Park had his fifth multipoint game and has three points in his last two games.
Jean-Sebastien Giguere made 28 saves for Toronto.
With both teams coming off games Saturday, Toronto jumped to an early lead off Kulemin's breakaway goal 57 seconds in. Defenseman Mikhail Grabovski caught the defense pinching in and hit Kulemin with a blue-line breakout pass. Kulemin took the feed in stride and lifted a wrist shot over Biron's stick for his second goal in two games.
Jackman and Park responded by scoring 6:04 apart. Almost 2 minutes after the Maple Leafs struck, Jackman tipped in a rebound between Giguere's legs.
Park picked up the assist on Jackman's goal, and added his short-handed goal at 8:55, wristing a high-slot shot past Giguere.
New York limited Toronto to seven shots in the second period, while Nielsen's goal with 1:38 left extended the lead to 3-1.
In the third period, Moulson scored his team-leading 25th goal, tipping in Josh Bailey's centering pass for a power play goal with 2:20 left.
NOTES: New York recalled rookie winger Mike Martin from the AHL before the game. Martin replaced LW Jeff Tambellini, who sat out with a strained groin. ... LW Trevor Gillies picked up the secondary assist on Park's goal for his first NHL point.