"They missed the puck in our zone, and I had full speed so it was kind of a pretty goal," Ovechkin said. "I'll take it."
Ovechkin picked up a loose puck near the boards and made a mad dash down the beating goalie Nathan Lawson with a backhand shot for a classic highlight goal after a mostly quiet game.
"I thought he looked lethargic a little bit," Washington coach Bruce Boudreau said. "Some superstars don't play good, but that's why they're superstars. ... because they rise to the moment at the right moment."
Lawson made 40 saves and kept the Caps at bay until Laich scored with 47.2 seconds left in regulation to force overtime. Laich redirected a pass from recently acquired Jason Arnott into the net.
"That was huge," said Washington goalie Michal Neuvirth, who made 28 saves. "After [Laich] scored, I knew we were going to win this game no matter what."
Washington improved to 11-0-3 in its last 14 games against the Islanders, who have lost four straight overall.
Matt Moulson's second-period goal nearly held up for New York in this game. He took a quick crossing pass from P.A. Parenteau and fired a shot past Neuvirth inside the right post for a 1-0 lead with 9:52 left in the second period. It was his team-best 28th goal.
Despite a 42-29 edge in shots, the Capitals just couldn't figure out many ways to beat Lawson, who made a number of tough stops. Washington kept the pressure on, but Lawson kept coming through.
Boudreau put Sturm on the top line with left wing Ovechkin and center Nicklas Backstrom. The coach also placed Arnott on the second line between left wing Laich and right wing Alexander Semin. Wideman was paired with veteran Scott Hannan on defense.
Sturm and Arnott both nearly scored in the opening minutes. Lawson stopped Sturm on a breakaway -- started by a long cross-ice pass from Ovechkin -- just over two minutes into the game.
Arnott then nearly redirected a shot past Lawson a little over a minute later, but the goalie caught it. Wideman also helped out when the Capitals needed to kill off penalties, and all three joined in on the power play.
Arnott came close early in the third period when Lawson stopped a wrist shot, and the puck trickled away but just missed the net.
The Caps tried to rally several times in the third period but kept coming up short. Backstrom drew a pair of minor penalties in the final seven minutes that forced the Capitals to go short-handed for four minutes.
But they finally got going in the final minute. After Boudreau had pulled Neuvirth for an extra attacker, Arnott got a loose puck behind the New York net and made a quick feed in front to Laich, who redirected it in.
That forced overtime and set up Ovechkin's ninth game-winning goal this season. He also assisted on the Laich goal -- the 300th of his career.
"It's extremely disappointing to lose it in the last 47 seconds," Lawson said. "We battled so hard for 59 minutes. To come away with just one point is unacceptable."
Arnott needs two more points to reach 900 for his career ... This was Neuvirth's 20th win of the season. ... The Islanders had lost a league-high 444 man-games to injuries heading into this game. ... Moulson now has played in 146 consecutive games, never missing one as an Islander.