Josh Bailey tied it 2-2 at 17:02 of the third period, collecting an errant pass from Toronto goalie Erik Kallgren and scoring from the right circle.
"At that point in time, you just give it what you've got," Bailey said. "We were fortunate to get a bounce and tie it up, and then get a great goal in OT. When you are down one, you are never out of it."
Noah Dobson had a goal and an assist, and Ilya Sorokin made 30 saves for the Islanders (12-8-0), who lost their previous two games and finished 2-2-0 on a four-game road trip.
Bailey was a healthy scratch for the first two games of the trip.
"Sorokin was great for us, as per usual, and gave us a chance," Bailey said. "I think we were all a little bit tired. We've been on the road for a little while, but that's part of playing in this league, you just have to grind it out some nights. We just stuck with it, and we were fortunate to find a way to get a win."