Mantha had his third multipoint game to tie Alex Ovechkin and Dylan Strome for the team lead. McMichael had his second multipoint game.
Aliaksei Protas added two assists and Charlie Lindgren stopped 37 shots to help the Capitals snap a two-game losing streak.
Arthur Kaliyev scored for the Kings and Cam Talbot made 13 saves. The Kings lost for the first time in regulation when scoring first, dropping to 11-1-1.
McMichael scored the go-ahead goal with 90 seconds remaining in the second period when he batted the puck out of the air and into the net after Talbot made a pad save on a shot by Mantha.
Anze Kopitar appeared to tie it 2 with 8:30 left in the third with a one-timer from the right faceoff circle, but Washington was successful in a challenge when the Kings were ruled offside.
Kaliyev extended his points streak to three games when he played Andreas Englund’s shot off the boards and put it past Lindgren at 9:04 of the first period. Kaliyev has five goals — two in the last three games.
Mantha tied it three minutes later, taking McMichael’s feed and finishing off a 2-on-1 rush for his fourth of the season.