The Rangers' checkmark for the playoffs will have to wait at least another day.
The Ducks scored two goals in 1:56 early in the third period to break a 3-3 tie, on their way to handing the Rangers a 6-3 loss.
New York's magic number to clinch a playoff berth remains at two.
With the teams tied, Ryan Kesler fired a shot right off the faceoff that was stopped, but Andrew Cogliano drove to the net and buried the rebound to put the Ducks ahead 2:19 into the third.
Patrick Eaves scored his second of the night less than two minutes later when his shot banked in off Brady Skjei's skate and into the net to put the Ducks ahead by two.
"We let our guard down on a couple plays and they made us pay," said Ryan McDonagh, who was a minus-1 in 22:16 of ice time. "We weren't pretty sharp with our passing and they looked a step quicker than us as far as coming up with pucks and controlling the play a little bit more.
"That's disappointing," McDonagh added. "Overall not a great game by us."
Video: NYR@ANA: Nash beats Bernier five-hole to open scoring
The Rangers and Ducks traded goals through the first 40 minutes of the game, starting with Rick Nash's fourth goal in as many games 5:54 into the contest.
Eaves tied the game three minutes later before Derek Stepan put the Rangers back up a goal with one of the prettier tallies of the season. Chris Kreider led a 3-on-1 rush and fed Mats Zuccarello, who sent it right back to Kreider, who then hit Stepan with a centering pass for the 2-1 lead.
Video: NYR@ANA: Stepan finishes tic-tac-toe passing play
Kesler scored on the power play to knot things at 2 with 2 minutes remaining in the first.
Anaheim took the lead for the first time 9:39 into the second period on a shorthanded goal by Josh Manson, but Skjei's fifth of the season at 13:10 knotted things for the third time.
After Anaheim's pair, Stepan nearly netted his second of the night when his shot from the faceoff circle hit not one but all three posts with just over 6 minutes remaining in the game.
Nick Ritchie capped the scoring with an empty net goal with 1:38 remaining.
Stepan said it was difficult for the Rangers to regroup after the early two goals that turned a tie game into a two-goal deficit in the blink of an eye.
"Bang bang play like that. When it's 3-3 and then it's 5-3 … it's not easy to adjust," he said. "After that, they just defended and we weren't able to generate enough."
Henrik Lundqvist, who missed the last eight games recovering from a hip strain, made 27 saves in the loss.
"Overall I felt OK," Lundqvist said. "A couple reads I could do better. Obviously the odd-man rushes and how aggressive I should be and read that."
Coach Alain Vigneault said too many players did not bring their best game against the now division-leading Ducks.
"At the end of the night we had too many guys that just brought a C-Game tonight and that's not good enough against a team that's playing as good enough as they are right now."
New York will have another opportunity to secure its spot in the Stanley Cup Playoffs Tuesday night when they finish their road trip against the San Jose Sharks.