Trailing 2-0 in the third period, the Capitals got consecutive goals from Troy Brouwer to tie it up -- the second coming with only 26 seconds left in regulation.
Then in overtime, Ovechkin picked up a loose puck in his own end, skated untouched into the Islanders' zone and fired a wrist shot from the left circle that got past Evgeni Nabokov for the game-winner.
Washington notched its third straight victory with the help of 22 saves from Michal Neuvirth.
Nabokov finished with 31 save for the Islanders.
Matt Moulson and Josh Bailey scored for New York.