"It's been up and down for us this year, and we've dealt with some adversity," Hanifin said. "With Darryl coming in and stuff, we've rebounded pretty well and put together a few big games. It's nice to see we're playing the right way too. We're working hard. We're playing a full 60 [minutes]. We're competing. Those are the signs you want to see. I think we're heading in the right direction."
Sutter replaced Geoff Ward on March 4. He was 107-73-15 with 15 ties in three seasons as Calgary coach from 2002-06, including advancing to the Stanley Cup Final in 2004, and was their general manager from 2003-10.
Elias Lindholm, Dillon Dube, and Andrew Mangiapane each had a goal and an assist for the Flames (14-12-3). Jacob Markstrom made 28 saves.
"It's fun. Winning is good," Dube said. "It makes it a lot easier coming to the rink for practice, and the energy stays a little higher."
Leon Draisaitl scored for a fifth straight game for the Oilers (18-13-0), who have lost two in a row after a four-game winning streak. Mike Smith made 23 saves.
The teams will complete a two-game set here Wednesday.
"It's a rivalry game," Edmonton defenseman Adam Larsson said. "It means a lot to both teams, the pride that's going into that. But I think we just need to find ways to win games no matter who we play.
"I still think we're doing a lot of good things. We're getting enough chances to win games. Today we came up short, [but] we're still a confident group. We just have to play a lot harder, but I still think we played well enough to win."