Mark Jankowski scored, and Smith made 22 saves for Calgary (50-25-7), which clinched the Western Conference on March 31. The Flames will face the Colorado Avalanche in the first round.
"The fun's just about to start here," said Calgary forward Johnny Gaudreau, who had an assist and finished the regular season with 99 points (36 goals, 63 assists). "We're looking forward to playoffs here and get things going."
The Flames will have home-ice advantage for as long as they remain in the first three rounds of the playoffs.
"We're ready, the fans are ready, the city is ready," Calgary defenseman Travis Hamonic said. "You can feel the buzz around the rink, around the city. When you're driving, everyone has the flags on their cars. That's awesome. This is the time of year. The weather's nice. You're playing these games and the whole city is behind you."
Draisaitl scored on a wrist shot 10:55 into the first period to give Edmonton a 1-0 lead. He is the first Oilers player to have 50 goals in a season since Wayne Gretzky and Jari Kurri in 1986-87. Draisaitl finished second in the NHL in goals, one behind Alex Ovechkin of the Washington Capitals.
"It's exciting, obviously," Draisaitl said. "It was something I've been working on and something that I've always obviously wanted to hit coming into this last game here. Guys kept trying to set me up. Luckily, one squeaked through."
Jankowski tied it 1-1 at 15:57 of the first when he tipped Hamonic's point shot.