Leo Carlsson powered Anaheim's offense in regulation, factoring in on each of the club's first four goals for his first career four-point game.
Cutter Gauthier and Olen Zellweger scored late third-period goals to spark the Anaheim comeback. Alex Killorn added a shorthanded tally, while Trevor Zegras and Pavel Mintyukov each collected assists.
Goaltender Lukas Dostal earned his career-best 21st win of the season with 27 saves.
Adam Fox, J.T. Miller, Alexis Lafreniere and Mika Zibanejad scored for the Rangers, who fell to 34-32-7 with the club's fifth loss in the last six games. New York remains out point out of the Eastern Conference's Wild Card spot. Former Vezina Trophy winner Igor Shesterkin took the loss in net with 28 stops.
Fox put New York ahead first just over three minutes into the action, winning the race to an errant shot off the end wall and lifting home the rebound over a sprawled Dostal.
Fox, a Long Island native, ranks among the NHL's top-10 scoring defensemen this season for the fifth straight year. The three-time All-Star has collected 13 points in 10 career matchups against the Ducks.
Anaheim briefly pulled even later in the first on a shorthanded rush, with Carlsson springing Killorn for a partial breakaway. Shesterkin would make the initial save on Killorn, answering a forehand move with a pad save, but the veteran winger followed up the rebound and tucked it just inside the near post before Shesterkin could slide across his crease.