Barrie gave the Oilers a 1-0 lead when he one-timed a pass from McDavid for a power-play goal at 12:00 of the second period.
"There's lots of good things that happened tonight," McDavid said. "I thought up and down throughout our lineup, everyone was solid. Guys were creating chances."
Jesse Puljujarvi one-timed McDavid's pass from behind the net to make it 2-0 at 6:37 of the third period.
Alex Chiasson redirected Barrie's one-timer for a power-play goal at 12:57 for the 3-0 final.
Oilers forward Leon Draisaitl had two assists; he's second in the NHL with 63 points (22 goals, 41 assists).
"They have a dynamic power play," Jets forward Adam Lowry said. "They've capitalized on multiple opportunities on that. Kind of just shutting down their two big guys, they always seem to find the score sheet. That's going to be one of our challenges moving forward, how to neutralize them a little bit.
"I think we have the guys in here, we have the team that can do that. It's going to be working out those kinks moving forward and getting ready for the next two that we play them (April 26 and 28)."
Winnipeg outshot Edmonton 13-3 in the third period.
"I thought we didn't move the puck particularly well," Jets coach Paul Maurice said. "That's going to be a real key to keeping those two quiet. But the rush game is going to disappear for just about everybody once the playoffs start."
NOTES: Among seasons in the NHL expansion era (since 1967-68) that played a schedule of 56 games or fewer, McDavid is the third player to score 70 points, joining
Eric Lindros
of the Philadelphia Flyers (70 in 46 games) and
Jaromir Jagr
of the Pittsburgh Penguins (70 in 48 games). Each accomplished the feat in 1994-95. … Scheifele (two goals, six assists) and Jets forward Nikolaj Ehlers (five goals, four assists) each had his point streak end at six games. … Barrie has scored five points (one goal, four assists) in his past four games. … Draisaitl has scored nine points (three goals, six assists) in his past six games.