Richards supplied the game's initial goal in the first period on assists from Rick Nash and Derek Stepan, and Nash again set up Richards midway through the second for a 2-0 New York lead.
The Kings' Jake Muzzin found the net 1 1/2 minutes later, cutting the deficit to one goal, but the Rangers added an insurance tally in third on a strange short-handed score.
On the play, New York's Ryan McDonagh sent a clearing pass from his own zone off the sideboards, which bounded slowly to toward the LA net. Goalie Jonathan Quick came out to steer it aside, but dropped his stick, and the puck bounced off his blocker pad straight into the net.
Henrik Lundqvist stopped 28-of-29 shots for New York, which logged its first win of the season.
Quick finished with 25 saves for the Kings, who fell in their home opener.