Jets defencemen Zach Bogosian had raced down the ice to grab a loose puck behind the net, but when he turned to clear it up the ice, he fanned on the shot and the puck went to Perry in front of the net.
The Ducks winger quickly put a high shot above goalie Ondrej Pavelec at 14:29 to the groan of fans at MTS Centre.
Goalie Viktor Fasth made 15 saves in a win that lifted Anaheim's record to 2-1-0. Pavelec faced 33 shots as the Jets went to 2-1-0.
Mathieu Perreault and Andrew Cogliano also scored for Anaheim, which concluded a season-opening, three-game road trip.
Andrew Ladd had a pair of goals for Winnipeg and Blake Wheeler assisted on both of them in his 375th NHL game.
Some of the game's loudest cheers were aimed at Anaheim forward Teemu Selanne, who began his NHL career with Winnipeg in 1992-93 by setting rookie records of 76 goals and 132 points during a campaign fans have never forgotten.
The crowd gave a roaring cheer during the singing of the American national anthem when the videotron showed the 43-year-old Finnish Flash.
Selanne also got a standing ovation midway through the first period after the announcer at MTS Centre noted his storied career, which Selanne has said will end after this season. He stood up from the bench and acknowledged the cheering with a wave of his glove.
After playing 231 games in a Jets' uniform, Selanne was traded to Anaheim in February 1996 and didn't get to move with the Jets when they relocated to Phoenix and became the Coyotes at the end of that season.
Anaheim doesn't play in Winnipeg again this season unless the teams face each other in the playoffs.
Even though they were outshot 15-6 in the first period, the Jets held a 2-1 lead on Ladd's goals after the opening 20 minutes.
Ladd deflected Wheeler's wrist shot just 11 seconds into a power play to make it 1-0 at 9:06.
But Ducks centre Perreault tied it up a minute and 10 seconds later when he flipped in a loose puck despite Pavelec's best efforts to stop it.
Ladd got the go-ahead marker at 16:17, catching Fasth out of position. After the puck bounced off the backboards, Fasth slid to the other side of his crease, but Ladd had quickly shot the puck into the open side.
The Jets didn't get a shot on net until almost five minutes into the scoreless second period and couldn't capitalize on three power-play opportunities.
Just 22 seconds after Winnipeg's third power play ended, Cogliano redirected a Dave Winnik shot to even the game 2-2 with four seconds left in the second. Anaheim's shot spread increased 25-12.
The Jets didn't get their first shot on goal in the third period until almost seven minutes in, with Pavelec facing four shots in the same span.
Notes: Winnipeg defenceman Tobias Enstrom has four assists in his first three games … Bogosian was playing in his 300th NHL game. He was drafted by Atlanta in the first round, third overall, in the 2008 entry draft ... The Ducks will mark the 20th anniversary of their inaugural NHL game on Oct. 8. They will celebrate at their home-opener on Oct. 10.