David Perron extended his NHL career-high point streak to 11 games with a goal for the Blues (20-20-4), who have won five of seven. Jake Allen made 28 saves.
"We've said all year long we've needed to string some wins together, especially with the start that we've had," Allen said. "We're still in the thick of things, really. We're not that far out of it, we've still got a couple games in hand and hopefully we can continue and cap off this road trip on the right note."
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Alex Ovechkin scored a power-play goal for Washington (27-13-5), which has lost two straight. Ovechkin passed Brendan Shanahan (238) for sixth place in NHL power-play goals and tied Dave Andreychuk (640) for 14th place in goals.
"We didn't play the right way, we didn't play well, and you can see the result," Ovechkin said. "All of us. It was bad play, bad game. Forget it, and tomorrow is a new day."
Pheonix Copley made 33 saves against his former team, and Washington defenseman Brooks Orpik played his 1,000th NHL game.
Allen won for the second time since Dec. 27.
"He was really sharp for us tonight and it was great to see for sure. He kept us in the game," Perron said. "Early even, that bomb from Ovechkin, I don't think many goalies would have stopped that."
The Capitals took a 1-0 lead when Ovechkin scored on a one-timer from the left circle at 7:50 of the first period off a pass from Dmitry Orlov. Ovechkin has three goals and two assists in his past five games and leads the NHL with 33 goals.