Rene Bourque had a goal and two assists, and Eric Nystrom and David Moss also scored to help the Flames improve to 7-2-1 with their third straight victory.
"He's hard to get off the puck," Dawes said about the 6-foot-2, 213 pound Bourque. "He's a great skater. He gets in there on the forecheck and when he gets the puck, he's got the long stick and a quick release. Obviously he's a playmaker as well."
The Flames are 5-0 against Northwest Division teams.
"These points are huge, especially early in the season," Bourque said. "It's going to be a long climb for some teams that are starting out slowly. It's hard to get points later in the year."
Dustin Penner scored his eighth goal of the season for Edmonton, and Lubomir Visnovsky added a goal. The loss snapped the Oilers' winning streak at three.
"We gave up two fast goals and then stopped playing," Edmonton coach Pat Quinn said. "We started to play solo hockey and that's not the way we're going to win and I don't know any team that does win that way."
Tied 1-1 after the first period, the Flames seized control in the second with three consecutive goal. They outshot the Oilers 19-9 in the period.
Calgary took its first lead at 3:53 when Dawes got open behind defenseman Theo Peckham and had an empty net as Bourque neatly set him up from behind the net.
Dustin Boyd created the next goal by stripping the puck from defenseman Tom Gilbert and taking the puck to the net, where his rebound was jammed in by Nystrom.
Calgary made it 4-1 at 10:23 of the second on a waist-high deflection by David Moss off a slap shot from Dion Phaneuf. The goal came on the first man advantage of the night for Calgary, which entered the game tied for first in the NHL on the power play.
The Flames ended up 2 for 4 with the extra man while Edmonton was 2 for 8.
Nikolai Khabibulin made 33 saves for Edmonton. ... With forwards Mike Comrie and Gilbert Brule out with the flu, Edmonton dressed seven defensemen, including Theo Peckham. He was recalled Friday from Springfield of the AHL.