Ovechkin scored career goal No. 791 at 12:24 of the third period, firing a quick wrist shot from the left circle past Calgary's Jacob Markstrom on the power play to secure the Captials' second straight win.
''When you win, you always have confidence. Sometimes you play well, but you can't win the game, and that's frustrating a little bit,'' Ovechkin said. ''But the situation right now, we just have to collect the points. It doesn't matter how: lucky, bad bounce. We just have to collect the points and try to get as many as possible.''
Ovechkin is now nine goals away from 800 and 11 from passing Gordie Howe for second place on the NHL's all-time goals list.
Oshie opened the scoring early in the first period, marking the first time since Nov. 11 that Washington scored the game's first goal. He has four points in back-to-back games since returning from a lower-body injury that sidelined him for 11 games.
''He's one of our leaders on the ice and off the ice. He brings a lot of energy,'' Ovechkin said of Oshie.
Evgeny Kuznetsov scored in the second period, picking up the puck from Oshie in the neutral zone, getting through three Flames and sliding the puck past Markstrom while falling.
Calgary had its share of scoring chances and outshot Washington 32-25, but Capitals goalie Darcy Kuemper earned his second shutout of the season.
''We've been talking about stringing a few wins together, so that was the focus tonight, just to come in and kind of do my job and help the team the best I can,'' Kuemper said.
Markstrom had 22 saves in the loss for Calgary.
''I think they were better with the puck than we were. That was the difference,'' Jonathan Huberdeau said. ''We had chances and didn't capitalize on it, and they did.''
Flames: Brett Ritchie returned after missing the last two games with an injury.
Capitals: Sonny Milano picked up two assists and has three points in his last two games. ... Dmitry Orlov missed his ninth straight game with a lower-body injury.
Flames: Visit the Carolina Hurricanes on Saturday to wrap up a six-game trip, their longest of the season.
Capitals: At the New Jersey Devils on Saturday to open their own six-game trip.
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