The score was tied 2-2 with 3 1/2 minutes left in regulation when Winnipeg defenseman Zach Bogosian carried the puck behind his own goal on a routine play.
But when he tried to make an outlet pass, he partially fanned on it and fell down, sending the puck dribbling in front of the net. It went right onto the stick of Perry, who buried a shot past Ondrej Pavelec.
Mathieu Perrault and Andrew Cogliano also scored for the Ducks, who won a second game in two nights.
Viktor Fasth stopped 15-of-17 shots for Anaheim.
Andrew Ladd scored twice in the first period for the Jets, who lost following two straight victories to begin the season.
Pavelec made 30 saves for Winnipeg.