Nugent-Hopkins scored with 18 seconds left in the second to make it 3-1, taking a pass from Jesse Puljujarvi and shooting over Rittich's shoulder.
"Our play wasn't good enough, and that's what got us into a 3-0 hole," Lucic said. "It was a really good play at the end of the second to give us some momentum going into the intermission. We had lots to look forward to going into the third."
Koskinen made the save against Derek Ryan on a shorthanded breakaway at 3:29 of the third period, and Lucic scored on the power play to make it 3-2 at 4:16.
Backlund scored unassisted at 14:15 to give the Flames a 4-2 lead. He intercepted a pass from Oilers defenseman Caleb Jones and scored from the right circle.
"We were really coming on and we had them on their heels," Hitchcock said. "Those are lessons that, unfortunately, you have to go through. It's a tough lesson, he'll learn from it, and he'll get better from it. We were mounting a comeback, and that one kind of took the wind our sails."
Monahan scored on the power play at 16:03 for the 5-2 final.