Tatar took a cross-ice pass from Dylan Larkin and slid a backhander past Washington goalie Braden Holtby for the game-winning goal.
In addition, Tatar scored twice in the other meeting between the two teams earlier this season, a 4-3 Washington victory.
The Red Wings appeared to be in charge after outshooting the Capitals 17-2 in the second period and getting goals from Luke Glendening and Anthony Mantha nine seconds apart with Tatar adding another 2:47 later for a 4-1 lead.
Detroit was coming off of a 7-6 overtime loss versus the Islanders where the Red Wings blew a 5-2 third-period lead.
This time, the Wings lost the 4-1 lead as Brett Connolly, Dmitry Orlov and Nicklas Backstrom scored third-period goals and forced overtime.
Backstrom's goal came with 17 seconds remaining while Washington had a two-man advantage.
Detroit goalie Jimmy Howard finished with 23 saves in the win.
For Washington, Alex Ovechkin did not get a shot in Friday's 4-2 victory over the Blue Jackets but scored this game's first goal, his 33rd this year -- matching his total for all of last season.
Washington helped the Red Wings a bit later in the period. Matt Niskanen of the Capitals fumbled the puck away in the neutral zone, and Justin Abdelkader picked it up and scored on a breakaway with 6:23 left, tying the score at one.
Niskanen also had the puck stolen from him on the third Detroit goal later on.
--Field Level Media
Detroit | Washington | |
Tomas Tatar 2 | Points | Alex Ovechkin 2 |
Tomas Tatar 2 | Goals | Alex Ovechkin 1 |
Nick Jensen 2 | Assists | Jay Beagle 2 |
N/A | Power Play Goals | Alex Ovechkin 1 |
N/A | Short Handed Goals | N/A |
Jimmy Howard .852 | Save Percentage | Braden Holtby .828 |
Jimmy Howard 23 | Saves | Braden Holtby 24 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Detroit | 29 | 5 | 0-3 | 1-3 | 6 | 29 |
Washington | 27 | 4 | 2-3 | 3-3 | 6 | 30 |