Nikolai Zherdev completed the scoring in the final second, when he was on a breakaway and Pronger tripped him. Because there was an empty net, Zherdev was awarded the goal.
Chris Drury had the Rangers' first goal, and Henrik Lundqvist made 19 saves.
Chris Kunitz scored for Anaheim.
The Rangers' victory in a rare appearance in Anaheim snapped the Ducks' five-game home winning streak.
Hiller, who made 27 saves, started for Anaheim. Jean-Sebastien Giguere, whose father, Claude, died in Canada on Monday, was given the night off.
Giguere, who recently visited his gravely ill father, remained on the bench as the backup. He is expected to leave the team later this week for the funeral and probably will miss Friday night's game at Edmonton before returning.
Kunitz tied it 1-all with his eighth goal at 18:30 of the second period. Lundqvist swatted away Ryan Carter's slap shot, then sprawled backward to bat away Bret Hedican's shot on the rebound, only to have Kunitz finally knock the puck past him.
Drury scored at 2:26 of the second after intercepting Scott Niedermayer's cross-ice pass inside the Ducks zone. Drury, all alone, got off a quick slap shot that sailed past Hiller.
The goal, Drury's ninth of the season, was his first in 12 games dating to Nov. 19.
Notes: The Rangers have played in Anaheim only three times in the past eight years, most recently when they won 4-3 in overtime on Nov. 1, 2006. ... The Ducks are 8-2-3 in their last 13 games against the Rangers, but have not beaten New York in Anaheim (0-2-1) since Dec. 15, 2000.
