Just 1:22 seconds later, Tkachuk and former Flame James Neal had a go, a longer tussle that went the length of the Flames bench as they threw punches and jostled.
Smith, who turned aside 20 attempts by the Flames in the first, made a tough late blocker stop on a shot by Mikael Backlund that went off the skate of Oilers blueliner Kris Russell's skate and changed direction to keep the homeside trailing by just one after the opening frame.
The Oilers got their first powerplay 2:35 into the second period, Brett Ritchie sent off for interference on Jujhar Khaira.
Markstrom made two massive saves on the three shots Edmonton got on the man-up, one on a tip in tight from Leon Draisaitl and then another coming across his crease to deny a one-timer slapper from Draisaitl in almost the exact same spot Gaudreau scored from.
Chris Tanev then added to the Flames hit count with a massive open-ice crunch on Kyle Turris just as the Oilers forward skated over the Calgary blueline, sending him crashing to the ice.
An ongoing game-long battle between Mangiapane and Draisaitl led to Calgary's second PP when the Edmonton forward went off for a cross-check at 6:48. The Flames managed three shots with excellent puck movement but Smith again stood tall.
Jesse Puljujarvi tied the game up with 2:59 left in the middle stanza, cashing in the rebound of a Russell point shot that was almost blocked by Lindholm, just squeeking through his legs on the way to the net. McDavid got the other assist, breaking out of a three-game pointless drought for the league's top scorer.
Smith made another big stop with less than a minute left off on a 3-on-2 Calgary rush, Mangiapane taking a pass from Lucic and firing a off-speed wrister that the Edmonton 'tender got a piece of with his glove to hold onto against his body.
Hanifin scored his first of the season - and first against the Oilers - 1:42 into the third, following an absolutely monster shift by the Flames. Tkachuk and Dillon Dube did the yeoman's work behind the net as they kept the pressure on, Hanifin eventually beating Smith five-hole, Lindholm and Dube getting the assists.