McDavid drew first blood in the first period.
During a shift in which the Oilers had sustained pressure around the Flames' net, the puck bounced out to him, courtesy of Leon Draisaitl. Uncovered, McDavid had an open net to shoot at to put his team up 1-0.
He added to the lead in the third period, roofing the puck over Smith to put the Oilers up by a pair. Smith had stopped him on two breakaways earlier in the game.
He added a late empty-netter with less than a minute to play.
The Flames had 26 shots of their own, with Mark Giordano, Sean Monahan, and Kris Versteeg leading the way with four shots apiece, but couldn't beat Cam Talbot.
Tanner Glass introduced himself to the Battle of Alberta, dropping the gloves with Zack Kassian in the first period and winning that bout as Kassian had to briefly leave the game for repairs.
The Flames' next contest will be their home-opener on Saturday, Oct. 7, as they host the Winnipeg Jets at the Scotiabank Saddledome (8 p.m.).
