Perry scored two power-play goals in a 1:35 span in the final period, and Curtis McElhinney made 34 saves in Anaheim's 3-2 victory Friday night.
Perry gave the Oilers the lead on a two-man advantage with 7:30 left when his shot deflected into the air and landed behind goalie Jeff Deslauriers before inching in.
Perry then added his 26th goal of the season, scoring off a scramble in front with 6:55 remaining. Teemu Selanne assisted on both goals.
With eight games left, the Ducks are 11 points out of the final playoff spot in the Western Conference.
"It's tough to say but our chances have slimmed down and we know that," Perry said. "But there are a lot of guys that are working for jobs and we're coming in every night and working hard and continuing to push. That's our attitude. Never say no.
"It can be tough mentally but you have to go out there and play your game. It's not over until you've played all 82 games."
Ducks coach Randy Carlyle said he expects his team to go out swinging.
"We won't accept anything less than 110 percent effort," Carlyle said. "That's what we have asked our players. We know it is difficult at this time but there are still people playing for jobs and opportunities for next year, and that's important."
Deslauriers made 37 saves for Edmonton. The last-place Oilers were coming off consecutive wins over Detroit, San Jose and Vancouver.
"It started off looking exactly like it was, two teams out of the playoffs and not caring how much they worked for the night," Oilers coach Pat Quinn said.
"If we have an attitude like that, even one single guy, then we have losers. That's the attitude you don't want any time. You can be in 30th. But you don't have to like it or play like a 30th-place guy."
Oilers defenseman Jason Strudwick said neither team seemed to have much jump.
"Quite honestly, I felt neither team came out with much of a sense of urgency," he said. "There were small burst from both squads and they got their power-play goals and that was the difference."
The Ducks were coming off losses in Calgary and Vancouver.
The Oilers will begin a four-game trip in St. Louis on Sunday night, while the Ducks will return home to play Dallas on Monday night. ... The Ducks have won the first three games of the four-game season series. ... Ducks scoring leader Ryan Getzlaf missed the game because of a sore left ankle. ... Former Boston University star Nick Bonino made his NHL debut for Anaheim. ... The Oilers signed former Michigan State defenseman Jeff Petry to a two-year NHL entry-level contract.