Ovechkin scored career goal No. 709 to surpass Mike Gartner for sole possession of seventh place on the NHL list. But New York stretched its point streak to four games, which includes three victories.
Ovechkin is eight goals away from Phil Esposito, who is sixth in league history with 717 goals.
''It's great to move on, I'm not done yet,'' Ovechkin said. ''I'm just trying to enjoy my time right now and enjoy this moment. Sucks we didn't get two points.''
Anthony Bitetto also scored for the Rangers and Artemi Panarin had two assists. Igor Shesterkin stopped 31 shots while recording his third straight win in as many starts.
''You can just see him getting more confident and settled in,'' Rangers coach David Quinn said of Shesterkin. ''If you are going to win a hockey game, your goalie has to make saves no matter what level you are at and our guy did tonight.''
Washington dropped its second straight game. Carl Hagelin also scored for the Capitals, and Vitek Vanecek had 27 saves.
Strome scored the deciding goal 7:55 into the third period, finishing an odd-man rush with Panarin. Kaapo Kakko also assisted on the play in his first game back after a brief stint on the NHL's COVID-19 list.
''Everybody is pulling their weight, we are playing as a team,'' Strome said. ''We are taking pride in the little plays, a penalty kill, a shot block. Earlier in the year guys were really just forcing offense. Now, when a guy makes a good play he is getting rewarded by his teammates, that goes a long way in a winning culture and that is starting to show in the results.''
Ovechkin got the Capitals within one with his third goal of the season at 11:01. The Capitals captain collected the puck shortly after an offensive zone faceoff and wired a wrist shot past Shesterkin.
''Alex was hunting the whole night, he was firing from all over,'' Capitals coach Peter Laviolette said. ''I've watched him for so many years from a different bench and to actually be on the bench and appreciate his talent is even more special. It's a great accomplishment for him.''
Bitetto gave the Rangers a 2-0 lead 9:15 into the second. The Long Island-born defenseman gracefully skated around the net before darting toward the slot and sliding the puck past Vanecek.
Bitetto was called up from the taxi squad earlier this week after the organization waived defenseman Tony DeAngelo following a postgame altercation between teammates.
''It was magical. I usually don't score those type of goals,'' Bitetto said. ''More importantly, we got a good win.''
Hagelin cut the Rangers' lead in half at 18:57 of the second. Garnet Hathaway fired a sharp-angled shot that deflected off Hagelin's glove and past Shesterkin. The play was reviewed but the call on the ice stood.
Strome opened the scoring 1:41 into the first. Adam Fox sent the puck toward the net from the blue line and Strome deflected it past Vanecek. Strome extended his point streak to four games.
''We have done that too much where we haven't played a 60-minute game,'' Hagelin said. ''It's time to adjust and figure that one out. If we do, we are a very successful team.''
Pavel Buchnevich added an empty-net goal in the final minute.
Defenseman Libor Hajek played in his first game of the season. The Rangers acquired the Czech defenseman in February 2018 as part of a larger deal that sent Ryan McDonagh and J.T. Miller to the Tampa Bay Lightning.
COMING OF AGE
Vanecek was named the NHL's Rookie of the Month for January after posting a 5-0-2 record with a 2.78 goals-against average and .918 save percentage in seven appearances. Vanecek became the eighth player in franchise history to earn the honor.
The Rangers were slated to play Saturday afternoon at New Jersey, but it was postponed due to a COVID-19 outbreak for the Devils. New York will have the weekend off before returning to action Monday night.
Rangers: Host Islanders on Monday.
Capitals: Host Flyers on Sunday.
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