Artemi Panarin scored his team-leading seventh goal and had an assist, and Taylor Ward, Mikey Anderson and Joel Edmundson also got their first of the season. Edmundson added an assist and Alex Laferriere had two. Darcy Kuemper made 23 saves.
The Kings (3-5-2) improved to 3-1-0 on their five-game road trip that concludes in Chicago on Tuesday.
The Rangers (7-6-1) lost their third straight game and for the first time at home (6-1-0).
James Reimer made his first start after the 38-year-old goalie signed a one-year contract with the Rangers on Sunday. But he allowed three goals on eight shots in the first period and was replaced by Dylan Garand to start the second.
Garand, appearing in his ninth consecutive game, made 15 saves. Adam Fox scored his first goal of the season in his 500th NHL game. Tye Kartye had a goal and an assist.
Ward gave the Kings a 1-0 lead at 1:15 of the first period. He got behind the Rangers' defense, took a pass in stride from Doughty and beat Reimer on a breakaway.
Brandt Clarke cashed in on a delayed penalty at 4:52, scoring from the left post to give the Kings a 2-0 lead. Joel Armia started the play when he put a sharp-angle centering pass cross-crease, which was deflected in by Clarke after a quick touch in front by Scott Laughton.
J.T. Miller had the puck go in off his right skate at 13:01 to cut Los Angeles' lead to 2-1, but Doughty scored on a one-timer from the point at 17:32 to extend the lead to 3-1.
Panarin greeted Garand with a power-play goal on a seeing-eye shot from the left face-off circle to give the Kings a 4-1 lead 90 seconds into the second period. Anderson got the puck off the face-off at the left dot in the offensive zone and put a slap shot past Garand to make it 5-1 at 6:54.
Fox scored from the point on the power play to make it 5-2 at 13:05 of the second.
Kartye cut the Kings' lead to 5-3 with a 6-on-5 goal at 16:08 of the third period, but Edmundson scored into the empty net at 16:37 for the 6-3 final.
