Connor McDavid, who also added two assists, had the other goal for Edmonton (6-3-0), which has won three in a row.
Stuart Skinner made 40 saves to earn the win and improve to 2-1-0.
Jacob Markstrom, who had 22 saves, suffered his first loss of the season. He is 4-1-0.
Looking to bounce back from a dismal playoffs performance against the Oilers last spring in which he gave up 24 goals in five games for an .852 save percentage, Markstrom was excellent for 2 1/2 periods stopping all but one of 23 shots as Calgary nursed a 2-1 lead.
Late in the second, he got his shoulder on a dangerous chance by Ryan Nugent-Hopkins after he was set-up by McDavid on an odd-man rush created by McDavid's stealing of the puck from Nazem Kadri in the neutral zone.
Five minutes into the third, the Oilers threatened again with Nugent-Hopkins again the triggerman in front, but Markstrom kicked out a pad to turn the puck aside and keep the score 2-1.
But at 9:02, Edmonton defenceman Cody Ceci rimmed the puck in from centre and after Markstrom went out of his net in an attempt to stop the puck behind the net but failed, he couldn't get back into the net and set and McDavid's quick shot went under his arm, tying the game.
On the game winner just over three minutes later, Edmonton pressure led to a turnover in front and McDavid's centring attempt deflected off Hyman's skate and into the net.
Calgary had broken a 1-1 tie 16:06 of the second on Ritchie's third of the season as the Flames' fourth line connected.
That's three goals in seven games for Ritchie, matching his goal total from last season, which came in 41 games. The rugged winger hasn't topped four goals in a season since 2017-18 with Dallas when he notched seven.
Scoreless after the first period, Calgary grabbed the lead short-handed at 4:14 of the second with Backlund getting loose down the wing and firing a shot past Skinner.
Less than 30 seconds later, Backlund got in alone, pulling Stewart out of position with a move to his left, but in attempting to set up Lindholm in front, the pass went into his skates and he wasn't able to get much of a shot.
Right after with the two Flames penalty killers caught up ice, Edmonton quickly transitioned up ice with Leon Draisaitl dropping the puck to McDavid who zipped a cross-ice pass to Hyman, who supplied the finish.
POWER PLAY SHOWDOWN
The game featured two of the league's top two power plays with Edmonton entering the night ranked second and the Flames sitting fourth. The Oilers went 1-for-4 making it nine games in a row with a goal on the man advantage.
Calgary, which is getting it done with a completely overhauled top unit with Nazem Kadri, Jonathan Huberdeau and Tyler Toffoli replacing Matthew Tkachuk, Johnny Gaudreau and Sean Monahan, went 0-for-3.
BATTLE OF ALBERTA NEARLY OVER
After finally meeting last year in the playoffs for the first time over 30 years, the two rivals only face each other three times this season and two of those games are now done.
Calgary won 4-3 two weeks ago in Edmonton. The season series wraps up Dec. 27 when the Oilers return to the Saddledome.
Oilers: Open a three-game homestand on Tuesday against the Nashville Predators.
Flames: Eight straight games at home continues Tuesday when the Seattle Kraken pay a visit.
This report by The Canadian Press was first published Oct. 29, 2022.
Darren Haynes, The Canadian Press