With New York's Blake Comeau off for roughing, Ovechkin whistled a long-range shot from just inside the blue line that tipped off Backstrom's foot and past Dwayne Roloson for his first goal of the season and Washington's third straight victory.
"I was just standing in front of the net there and [Ovechkin] was shooting at my feet," Backstrom said. "He hit my foot. It was kind of lucky he didn't hit it too hard, otherwise I probably couldn't walk tomorrow."
Backstrom, held without a point in Washington's first three games, finished with a goal and an assist -- and earned his way back to the top line after a brief demotion.
Boudreau had split up the first-line tandem of Backstrom and Ovechkin for the first period, hoping a brief hiatus would stop both players from pressing. The coach hopes the decisive goal Wednesday will wake up the Capitals' slumbering power play, which is 2 for 17 this season.
"It was just a matter of time," Boudreau said. "With the people you put out there, hopefully they simplify it and they got one at the right time."
Ovechkin also scored for Washington, his third straight game with a goal.
Nino Niederreiter scored for the Islanders, who lost in regulation for the first time in three games this season.
"We dominated in the first and third, but we cost ourselves with a goal there in the second period and that's something we can't have," Comeau said.
The Capitals are 8-0-3 in their last 11 games against New York.
Washington killed off three power plays and improved its penalty kill to 15 for 15 to start the season.
Niederreiter's first career goal staked the Islanders to a 1-0 lead 3:14 into the game. Darting uncovered through the right circle, Niederreiter quickly one-timed Doug Weight's feed from the right corner past Michal Neuvirth.
Boudreau shuffled his top two lines, opening the game with usual second-line center Tomas Fleischmann skating with the first unit in place of Backstrom, who was dropped to the second line.
But both Fleischmann and Backstrom returned to their customary lines by the start of the second period after the new alignment produced only five first-period shots.
"You get [Ovechkin and Backstrom] away from each other so they can continue to play their own game," Boudreau said. "Then, once they feel the confidence, you put them back. Once Nicky got the assist, I knew he was going to get more because he just never stops at one when he gets a little bit of a roll going."
The switch back produced the desired results, as Washington put 15 second-period shots on Roloson, tying the game on Ovechkin's goal 18:19 into the period.
From center ice, Backstrom fed Ovechkin just inside the blue line. Ovechkin corralled the puck, then used defenseman Mark Eaton as a screen to whip a shot from the left wing past Roloson for his fourth goal.
"This is our fourth year playing together and we understand each other a lot," Backstrom said. "Every time we have the puck, first of all, we see each other and try to find each other. It's good."
But the Capitals had to rely on Neuvirth, who made 12 of his 23 stops in the third period, to hold off the Islanders.
Frans Nielsen missed a chance to put New York ahead with 12:53 remaining in regulation when Neuvirth blocked his try at the right post. The Islanders' Matt Moulson got loose on a break with 6:04 to go, but Neuvirth knocked the puck away. Less than a minute later, Neuvirth thwarted Michael Grabner's cutting move from the left wing.
- RW D.J. King, Washington's new enforcer who played in his first game of the season, got into a fight only 2:47 into his Capitals career, squaring off against Islanders LW Trevor Gillies.
- Washington scratched D Tom Poti (lower body), RW Matt Bradley (lower body) and C Marcus Johansson (leg).
- C John Tavares (head) was out of the Islanders lineup.