The teams combined for five goals in 8 1/2-minute stretch of the final period, including a tying score by New York's Anders Lee with 2:40 left in regulation.
In the extra frame, Visnovsky intercepted a Maple Leafs clearing attempt and fired it home for the game-winner.
Michael Grabner scored a pair of short-handed goals as the Islanders broke a two-game slide in their first appearance following the Olympic break.
Evgeni Nabokov earned the win with 18 saves.
Jonathan Bernier was tagged for five goals on 35 shots.
Former Titans kicker dies in car crash
UPI Sports Results for September 20, 2014