Ovechkin capitalized on a Josh Bailey giveaway at 1:35 of overtime after Brouwer tallied twice in the final 3 1/2 minutes of regulation, giving the Washington Capitals an improbable 3-2 victory at the Verizon Center.
"It's a huge victory for us," Ovechkin said. "We needed one goal, and Browse gets it. He gets a second one and in OT, I had a lucky goal."
Blanked by New York goalie Evgeni Nabokov for 56 minutes, the Capitals mounted a stunning rally to win their third straight -- their longest streak since an identical run in mid-January.
Brouwer cut the deficit to 2-1 with 3:29 left in regulation, scoring from the right of the net after taking an excellent crossing pass from Mathieu Perreault.
"The first goal hurt," Isles coach Jack Capuano said. "It was a negated icing and we leave a guy alone in front of the net. That first one hurt bad."
After Capitals coach Dale Hunter pulled goalie Michal Neuvirth, Brouwer deflected a shot by Brooks Laich past Nabokov to tie it with 25.5 seconds to play after Isles center Frans Nielsen lost a crucial faceoff in New York's zone.
In overtime, Ovechkin raced into the New York zone from the left side and fired a wrist shot from the top of the left circle that found the back of the net.
"It's a big two points," Hunter said. "Their goalie was putting together a good game. You could tell he was having one of those games that it was going to take a special play to get a goal on him."
It was the fourth straight road loss for the Islanders, who were 13-1-5 when leading after two periods. Nabokov fell to 10-2 against the Capitals, who opened a five-game homestand in impressive style.
Washington was 0-2 this season against the Islanders, the only Eastern Conference team it had failed to defeat this season. The Capitals moved past Winnipeg into the eighth spot in the East with 69 points.
The Islanders, meanwhile, failed on a golden opportunity to pull within six points of the Jets while still having two games in hand. Instead, they're now in 14th place in the East.
"You've just got to regroup and come back and battle," Capuano said. "That's the way it goes. We had some chances."
Washington outshot New York 13-3 in the first period, but the Islanders took a 1-0 lead on Bailey's seventh goal of the season. Bailey faked a shot from the top of the right circle, then skated down the middle and deked Neuvirth before pumping in a wrister from the slot at 4:14.
It was the Islanders' second shot of the game; the next didn't come until 18:22. Washington managed only two shots during two power-play opportunities over the first 20 minutes.
The second period wasn't much different in that the Capitals still couldn't find a way to score. After New York took the first five shots of the period, Washington's Mike Green finally tested Nabokov with a long-range wrist shot at 9:03 during what turned out to be another futile power play.
"It's unacceptable to give up a two-goal lead that late," Bailey said after the Islanders lost for the seventh time this season after leading by more than one goal. "Breakdowns are a part of the game, but you certainly don't expect the outcome to be like that when you are up two goals."
Material from wire services and team media was used in this report.
Wrist shot -
1 - 0 NYI