Milan Lucic, Johnny Gaudreau and Dillon Dube each had a goal and an assist for the Flames, who trailed 2-1 after the first period.
''We talk about having more swagger when we get down in games,'' Backlund said. ''We don't want to get down in games, but we have lately.
''We've got to get that swagger back, that we know we're going to come back and we know we're a good team and it doesn't matter how games go.''
Calgary's Sam Bennett and Elias Lindholm also scored as the NHL's Battle of Alberta commenced in the pandemic-compressed 2020-21 season.
Jacob Markstrom made 28 saves for the Flames, including 16 in the first period when his team was outshot 17-3.
''It takes a lot of volume shooting to score on that guy,'' Oilers defenseman Adam Larsson said. ''He had a solid night.''
Oilers captain Connor McDavid had a goal and an assist, with Jujhar Khaira, Jesse Puljujarvi and Darnell Nurse also scoring for Edmonton.
McDavid extended his point streak to nine games (six goals, 15 assists) and still leads the NHL's points race with nine goals and 17 assists.
Oilers starter Mikko Koskinen stopped 22 shots in the loss.
''When you get six goals scored on you, there's a few things you need to clean up,'' Oilers defenseman Darnell Nurse said. ''We need to be better in our own zone, support each other in the middle of the ice and if we take care of that, we know we have enough offense.''
Saturday's meeting was the first of 10 this season between Alberta's NHL teams and the first since the two clubs combined for over 100 penalty minutes Feb. 1, 2020.
NOTES: Calgary placed C Derek Ryan (broken finger) on long-term injury reserve, while the Oilers put D Ethan Bear (upper body) on injured reserve Saturday. ... Gaudreau reached a career 300 assists. ... Calgary D Noah Hanifin played his 400th career NHL game. ... The Flames donned retro jerseys Saturday featuring the flame-snorting horse head ''Blasty'', which was first worn in 1988-89 to commemorate the Year of the Cowboy.
The Flames are at home against the Winnipeg Jets on Tuesday and the Vancouver Canucks on Thursday.
The Oilers head east on their five-game road trip for a pair of games in Ottawa and one in Montreal.
More AP NHL: https://apnews.com/hub/NHL
Copyright 2021 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.