Austin Wagner scored two goals for the Kings (23-28-5), who went 3-2-1 on a season-long six-game road trip. Tyler Toffoli and Oscar Fantenberg also scored, and Jonathan Quick made 25 saves.
"It was a tough trip. I thought we played real good the first game [a 4-2 loss against the New York Islanders], and we didn't get anything out of that one. But we bounced back, played good in the middle," Los Angeles coach Willie Desjardins said. "It was just a tough game tonight. We didn't seem to have our legs, but I thought the guys battled."
Ovechkin made it 1-0 at 3:07 of the first period with a one-timer from the left face-off circle on the power play for his first goal in five games since Jan. 23. He has 12 points (five goals, seven assists) in his past seven games.
The Kings tied it 1-1 when Derek Forbort sent a no-look pass across the crease to Wagner at 4:50.
"Obviously, some stuff happened today with the team and I was told to be ready to play tonight, so I was ready to go," Wagner said, referring to the trade of forward Nate Thompson to the Montreal Canadiens.
Connolly's third goal in two games gave Washington a 2-1 lead. Quick made a pad save on his initial shot, but Connolly roofed the rebound at 15:17.
Toffoli scored his fourth goal of the road trip when his one-timer from the slot during a power play tied it 2-2 at 17:22 of the first.
The Kings took a 3-2 lead at 3:42 of the second period when Fantenberg ended a lengthy stretch in the Capitals zone with a wrist shot through traffic from the point.