David Pastrnak took a stretch pass from Mark Kastelic at the blue line and quickly fed a streaking McAvoy, who beat Darcy Kuemper with a backhand deke.
McAvoy, who needed facial surgery after being hit by a puck in November, exited the game late in the second period but returned for the third, sporting an abrasion on his face.
Defenseman Mason Lohrei also scored for the Bruins (36-22-6), who have won 13 straight on home ice. Jeremy Swayman made 14 saves for his 25th win of the season, tying an NHL career high.
Drew Doughty tied it late in the third period for the Kings (26-23-15), who were coming off a 5-4 overtime win at the Columbus Blue Jackets on Monday. Kuemper made 22 saves.
Scott Laughton had a chance to give the Kings the lead while short-handed in the second period. After Hampus Lindholm whiffed on a shot from the point, Laughton collected the loose puck and broke in alone on Swayman, who made the save to keep the game scoreless.
Lohrei gave the Bruins a 1-0 lead at 8:22 of the third period. He received a pass from Lindholm and scored with a wrist shot from the top of the right circle that beat Kuemper blocker side off the post.
Doughty tied it 1-1 at 14:00. He skated in off the bench and had his one-timer from the right point deflect in off Elias Lindholm’s skate.
