David Perron opened the scoring for the Red Wings at 7:30 of the first period, then Oskar Sundqvist's power-play goal about eight minutes later in the same frame put Detroit ahead, 2-0.
After Washington recorded back-to-back tallies 11 seconds apart late in the second, Lucas Raymond's eight goal of the season early in the third reclaimed the lead, 3-2, for the Red Wings. The Capitals found the back of the net just 10 seconds after Raymond did, then scored the game-winner with 22 seconds remaining in overtime.
"I thought our overtime was the most chances we generated," captain Dylan Larkin said. "But they get a shot, it goes in and the game is over. It was a much better, much more productive overtime. We still need to find two points, but we feel it was a pretty good point tonight for us."
Goalie Ville Husso made 38 saves for Detroit (13-11-7; 33 points), which picked up a point but saw its winless streak stretch to six games. With the victory, Washington moved to 17-13-4 (38 points) on the season.
NEXT UP:The Red Wings will welcome the Tampa Bay Lightning to Little Caesars Arena on Wednesday night.