Currie was recalled from Bakersfield of the American Hockey League on Monday and was playing his third NHL game.
"It's super exciting. Words can't even describe how I am feeling right now," Currie said. "It is obviously even better to get the win. I wouldn't have wanted to get it with a different group of guys. It is awesome."
WATCH: [All Ducks vs. Oilers highlights]
Sam Gagner
scored, and Mikko Koskinen made 33 saves for Edmonton (26-29-6), which is seven points behind the Colorado Avalanche for the second wild card into the Stanley Cup Playoffs from the Western Conference.
Carter Rowney scored for Anaheim (24-29-9), which is eight points back of Colorado. Kevin Boyle made 19 saves.
"I thought it was kind of a weird game for me, personally," Boyle said. "For the first 10 or 11 minutes, I only had one shot, and so it was a little hard getting settled into the game. I thought once I got my first few shots under the belt I settled down a bit, especially going into the second and third period.
"The first 11 minutes I thought we dominated, we had some great chances, I thought their goalie played great and made some big saves for them. I thought we had our chances, we just have to bury them."