Carter and Richards each scored on the power play in the first. Carter also assisted on Richards' goal.
J.T. Miller scored for the Rangers (1-5), who played their fourth game in five nights, closing their western preseason trip.
New York opens the regular season at Phoenix on Thursday, while Los Angeles finishes the preseason Saturday.
After the Kings won the opening draw, Kopitar took the puck down the left boards, headed to the goal and beat goalie Henrik Lundqvist with a backhand.
Jonathan Quick had 22 saves for the Kings, while Lundqvist finished with 29 stops.
The teams play in the regular season on Oct. 7 in Los Angeles.
The Kings' victory was part of Frozen Fury 15 at the MGM Grand Garden Arena. The Kings play Colorado on Saturday night at the MGM Grand to conclude their preseason and Frozen Fury 15 stay in Las Vegas.
Kings captain Dustin Brown might play against Colorado. He has been out with a hamstring injury.