Fredrik Sjostrom and Blair Betts had short-handed goals for the Rangers, who head into the All-Star break having won four of their last five games. Henrik Lundqvist made 32 saves to earn his 24th win of the season.
New York regained first place in the Atlantic Division with 60 points, one more than the idle New Jersey Devils.
Bobby Ryan and Corey Perry each scored a goal for Anaheim. Anaheim goalie Jonas Hiller stopped 26-of-29 shots.