Anton Forsberg failed to cover up the puck after saving Morgan Geekie's shot from the left circle, allowing Matthew Poitras to knock it to Khusnutdinov, who got to the paint to backhanded it into the open net for his second goal of the season.
David Pastrnak had a goal and an assist to extend his point streak to five games, Elias Lindholm and JJ Peterka added late empty-net goals, and Jeremy Swayman made 25 saves for the Bruins (7-2-0), who have won five in a row, including 4-2 at the Anaheim Ducks on Friday.
Alex Laferriere scored the lone goal, and Forsberg made 24 saves for the Kings (0-4-2), who are still looking for their first win under coach Peter Laviolette.
Laferriere put the Kings up 1-0 just 31 seconds into the first period. His initial redirection of Brandt Clarke's point shot was stopped by Swayman, but Adrian Kempe got the rebound and passed back to Laferriere, who tapped it in from the top of the crease.
Los Angeles had moved Laferriere up to the first line with Kempe and Artemi Panarin in an effort to boost their struggling offense, which has scored one goal in each of the past four games.
Pastrnak tied it up 1-1 at 2:43 of the second period. He buried a wrist shot from the right circle off the rush after Erik Gustafsson couldn’t keep the puck in the offensive zone for the Kings.
Pastrnak has 10 points (four goals, six assists) during his five-game streak.
After Khusnutdinov put the Bruins in front, Lindholm (18:02) and Peterka (19:42) sealed the 4-1 final.