"It feels good when they stay out and you get a win like that," Miller said. "It's nice."
Washington controlled the majority of the play, registering 15 shots in the first three periods before adding five in overtime.
"We made the right decisions with the puck, and the power play was working today, but we didn't score," Ovechkin said. "(Miller) was on top of his game and he carried them into the shootout and onto victory."
Capitals coach Adam Oates had a hard time faulting his team after its dominant performance that didn't produce a win.
"I can't really complain," Oates said. "There's games that your goalie steals games for you, and I kind of look at that one as a game that their goalie did for them."
Washington had the first 12 shots, and with 13:52 gone, Miller stopped Eric Fehr from point-blank range to keep the Capitals off the board.
Buffalo finally put a shot on Grubauer with 4:23 left in the first. Matt D'Agostini's odd-angle snap shot was met with a loud cheer from the home crowd.
Grubauer said the lack of action didn't bother him.
"It's OK," Grubauer said. "You've got to face it shot by shot, and not look at different outcomes or how much time goes by. You just see it as a little break."
Ott took a cross checking penalty 5:53 into the game, but Washington's NHL-best power play couldn't take advantage. Miller made a shoulder save on a deflection by Mikhail Grabovski.
The Capitals had a 15-3 shots edge in the first period.
Grubauer stopped Grabovski and then foiled Matt Moulson with a left pad save in the crease off the ensuing faceoff.
Capitals forward Tom Wilson laid a heavy hit on Ville Leino late in the second period, and Marcus Foligno challenged him to a fight. Foligno was given an instigator penalty and 10-minute misconduct, putting Washington's power play back on the ice.
Despite being outshot 30-10, Buffalo took a 1-0 lead when Stafford tapped in Christian Ehrhoff's rebound with 1:42 left in the second.
"Christian's shot was an easy little wrister, and those are the ones that find their way through," Stafford said.
Grubauer made a glove save on D'Agostini moments later to keep the Capitals' deficit at one goal.
Washington tied it off a giveaway by Ott 5:34 into the third period. Brouwer's slap shot beat Miller over the right shoulder.
"Ott tried to backhand the puck, and it just slipped off the backhand of his stick," Nolan said. "When he makes a mistake it's not because he's not trying. It was a bad bounce for us."
Miller returned to form over the next few minutes, including three successive saves from a prone position.
"He's the best goalie in the league, and I don't say that lightly by any means," Ott said. "The team didn't steal the game, Ryan Miller stole that game for us."
Brooks Laich sat out a second consecutive game and for the 13th time in 14 games because of a groin injury. ... The Sabres used the same lineup from Friday's shootout loss in Toronto. ... Washington outshot an opponent for the first time in six games.
Copyright by STATS LLC and The Associated Press
BUFFALO, NY - DECEMBER 29: Joel Ward #42 of the Washington Capitals checks Marcus Foligno #82 of the Buffalo...