Tatar skated into the zone on a 2-on-1 with Dylan Larkin, who slid a pass to him at the left post, and Tatar cut back to the right and scored on a backhand.
The goal came after Nicklas Backstrom scored a 6-on-4 goal with 16.7 seconds left in regulation to tie it 4-4, capping a three-goal rally for the Capitals in the third period. The Red Wings were coming off a 7-6 overtime loss to the New York Islanders on Friday in which they blew a 5-2 third-period lead.
WATCH: [All Red Wings vs. Capitals highlights]
"I was worried it might be the same story as against the Islanders," Tatar said. "You don't want that to happen. It felt really bad after the game [Friday] and if you have two in a row like that, that would be just miserable. So, I'm glad we got the two points."
Luke Glendening, Anthony Mantha and Tatar scored consecutive goals in a 2:56 span during the second period, and Jimmy Howard made 23 saves for the Red Wings (22-23-9), who ended a three-game losing streak (0-2-1).
Alex Ovechkin had a goal and an assist, and Braden Holtby made 24 saves for the Capitals (32-17-6), who have lost three of their past five (2-2-1).
Ovechkin put Washington up 1-0 at 4:20 of the first period with a power-play goal off a one-timer from the left circle.
Justin Abdelkader tied the game 1-1 at 13:37, scoring on a breakaway after Matt Niskanen misplayed the puck at center ice.
Glendening's rebound goal at 16:53 of the second period put Detroit ahead 2-1, and Mantha scored nine second later from in front off a pass from behind the net by Henrik Zetterberg to make it 3-1.
Tatar extended the lead to 4-1 with 10.8 seconds left in the second on a late rush, taking a drop pass from Larkin and shooting over Holtby's glove.