Holtby made a blocker save on Mark Giordano's partial breakaway 10 seconds after Brouwer's goal and then Ovechkin zipped a shot from the faceoff dot over the glove of Elliott at 17:09 to push Washington's lead to 4-2.
"Myself, I had a really good chance to tie the game," Giordano said. "Those ones are tough when you didn't play your best but we had a look there. We've got to move on. We stuck with them. We had a good push right at the end of the game.
"I thought they were the better team."
Kuznetsov scored 6:47 into the game to put Washington up 1-0. Andre Burakovsky stripped Johnny Gaudreau of the puck in the neutral zone before setting up Kuznetsov with a tap-in, but Gaudreau fed Monahan on a 2-on-1 before Monahan ripped a shot by Holtby's blocker to tie the game at 10:06.
NOTES: Elliott's run of 11 straight wins tied a Flames franchise record set by Mike Vernon from Jan. 17-Feb. 27, 1989. He named the NHL's Third Star Of The Week on Monday. TJ Brodie led the Flames with 24:12 of ice time. Defencemen Michael Stone and Matt Bartkowski and forwards Freddie Hamilton and Lance Bouma each had three hits. Forward Matthew Tkachuk served the first part of a two-game suspension for elbowing Los Angeles Kings defenceman Drew Doughty on Sunday. Defencemen Dennis Wideman and Rasmus Andersson and forward Garnet Hathaway were scratched for Calgary.
UP NEXT: The Flames continue with the second of a three-game road trip at the Nashville Predators on Wednesday (6 p.m. MT; SNF, SN960).
(with files from Ty Pilson)