"These games always have a lot of energy," Eberle said. "More importantly, they're four-point games. These are divisional games, and when you can sweep a team that's in your division it sets you up well."
WATCH: All Oilers vs. Flames highlights
Brossoit, who made his season debut, was 0-5-1 to start his NHL career. He was selected by Calgary in the sixth round (No. 164) in the 2011 NHL Draft and acquired by Edmonton in 2013.
"It's a great feeling, especially with how last year went down with my call-up," said Brossoit, who started for the first time since March 26, 2016. "It's nice to contribute in a positive way."
Matthew Tkachuk, Sean Monahan and Lance Bouma scored for the Flames (24-22-3), who have lost four of five (1-3-1).
"It's embarrassing," Calgary coach Glen Gulutzan said. "It's embarrassing. I don't talk to the guys after the game, win or lose, I talk to them the next day, but certainly in the coaches' room, emotions are high. It's embarrassing."
Edmonton chased Calgary goaltender Chad Johnson by scoring on three consecutive shots in a 4:41 span early in the first period.
The Flames surrendered the first goal in their seventh straight game when Slepyshev scored at 1:17. Letestu followed at 5:22 and Eberle at 5:58 to chase Johnson, who made one save.
"It wasn't really what I had in mind and it wasn't really the game I don't think anybody pictured it to be," Johnson said.
Brian Elliott came in and finished with 23 saves.
McDavid shot by Elliott's blocker 3:57 into the second period to give the Oilers a 4-0 lead, and Eberle scored at 12:24. Eberle has three goals in three games to follow an 18-game drought.
"Once the puck goes in it starts to go in," Eberle said. "The biggest thing is you've got to continue to do the things that got you to the point when you're starting to put it in."
Tkachuk scored on the power play at 15:55 to cut the lead to 5-1, but Klefbom scored 58 seconds later.
Monahan scored for the fifth consecutive game with a shorthanded goal 26 seconds into the third to make it 6-2, and Bouma scored with 4:11 remaining.
Nugent-Hopkins scored into an empty net with 34.8 seconds remaining.
"It's frustrating and there's not much else to say," Monahan said. "It's a bad loss for us and now we have to regroup from that."
