Ovechkin's 23rd goal of the season came on a blast from the top of the right circle that beat Anaheim's John Gibson.
Washington took only 15 shots over the first 40 minutes and trailed 2-0 before Nicklas Backstrom knocked in the rebound of a shot by Ovechkin at 3:05 of the third period.
Evgeny Kuznetsov tied it just over four minutes later, beating Gibson on the stick side with a shot from the left circle.
Braden Holtby had 28 saves for the Capitals, who have won in a row and 10 of 12.
Washington never got a chance to unleash its power play, ranked seventh in the NHL at 20.8 percent. Anaheim was called for only one penalty, against Kevin Bieksa for fighting in the first period against Tom Wilson.
Derek Grant and Jakob Silfverberg scored for the Ducks, who opened a six-game road trip with a win in St. Louis on Thursday night. Anaheim appeared poised to build on that victory before Washington came back.
The Ducks went on the power play only once, and cashed in. Silfverberg made it 2-0 at 7:36 of the second period, deflecting a shot by Ryan Getzlaf just five seconds after Andre Burakovsky went to the penalty box for hooking.
Derek Grant got the scoring started at 16:01 of the first period, skating down the right side on a 2-on-1 with Dennis Rasmussen before flicking a shot past Holtby's right shoulder.