Ovechkin capitalized on a power play 13 seconds after Anders Lee was whistled for interference. He batted Thomas Greiss' attempted poke check out of midair, and the puck went off Johnny Boychuk's stick and over Greiss to give the Capitals a 2-1 lead.
It's the 10th time Ovechkin has scored 45 goals, passing Wayne Gretzky and Mike Bossy for the most in NHL history.
WATCH: [All Capitals vs. Islanders highlights]
"His ability to score goals, create offense is something that I have never seen before," Washington forward T.J. Oshie said of Ovechkin. "There are greats in the League, but none that I have seen that are such a natural prolific goal scorer. He does a lot of the heavy lifting for us. It goes to show how special of a player he is."
Jakub Vrana tied the game 1:08 prior to Ovechkin's goal, and Braden Holtby made 20 saves for Washington (37-21-7), which has won five of its past six games and is again tied in points with New York for first place in the Metropolitan Division. The Islanders have a game in hand.
"It was an extremely competitive game," Capitals coach Todd Reirden said. "I thought the intensity level was at a high. We didn't have success to start the game, but we stayed the course. We didn't change how we played. We continued to play the same way the rest of the game until we were rewarded.
"That's a big step in the overall growth of our game, to not start to cheat for offense or any of those things. We spent a ton of time in the offensive zone and carried a lot of the play. Eventually we earned a power play and were able to capitalize on some chances."
Oshie was credited with an empty-net goal at 18:32 of the third period when Islanders forward Josh Bailey accidentally put the puck in his own goal from just outside the defensive zone.
"It's on me, obviously," Bailey said. "Obviously, I was trying to give it over to (Brock Nelson). I just put it a little too hard. I've got to be better in that situation. When the game's on the line and the goalie's pulled, you've got to be sharp. That wasn't the case there."
Tom Kuhnhackl scored for the Islanders (37-20-7), who failed to deliver coach Barry Trotz his 800th NHL win. Greiss made 26 saves.