Three of Washington's goals came on special teams: two on the power play and one shorthanded.
"That's the difference in the game," Red Wings coach Jeff Blashill said. "Both teams scored a shorty, but we had one on the power play and they had two."
Darren Helm scored, and Mrazek made 37 saves for Detroit (4-3-1), which has lost three in a row.
"Obviously, it disappointing to be up that late in the game and not win," Tatar said. "We felt that was a game where we were going to get two points."
Burakovsky and Jay Beagle scored for Washington (4-3-1). Holtby made 34 saves.
Darren Helm made it 1-0 with a shorthanded goal at 4:31 of the second period. He intercepted Ovechkin's pass, accelerated past him on his way out of the zone and beat Holtby for his first goal of the season.
Burakovsky, who was dropped to the third line for the game, tied it 1-1 with 50 seconds left in the second, beating Mrazek with a wrist shot from the top of the face-off circle for his first goal of the season.