Blake Wheeler scored for the Jets (27-19-3), who have lost five straight games. Connor Hellebuyck made 24 saves.
"I thought we were hard tonight," Hellebuyck said. "We were doing all those details hard. It was a step in the right direction, but we can't settle for losing. We're going to snap out of this and it's going to be big, and we're going to carry that momentum. It's just a matter of time."
The Oilers have won four of their past five games and are in second place in the seven-team North, three points ahead of the Jets. The first-place Toronto Maple Leafs, who clinched a playoff berth Wednesday, are seven points ahead of Edmonton. The top four teams qualify for the Stanley Cup Playoffs.
Edmonton won seven of nine against Winnipeg this season.
"I don't know exactly what it is; we definitely raise our level when we play these guys," Nugent-Hopkins said. "I think overall we try to limit their high-quality scoring chances from in tight and try to keep it to the outside as much as possible, and we found a way to capitalize on our chances against them."
Barrie one-timed McDavid's feed for a power-play goal at 10:52 of the first period to give the Oilers a 1-0 lead.
Wheeler tied it 1-1 with a shot from the left circle at 4:29 of the second.
"It was way better than the last game for sure," Wheeler said. "We beat them 1-0 5-on-5, [but] they scored two power-play goals. Obviously, that was the difference in the game.
"We've got some important games [upcoming] for our group and it was a step in the right direction tonight, but nothing's going our way."