Kassian took offense to a hit from Tkachuk late in the second period and threw off his gloves and started punching the Flames forward, also tossing Tkachuk to the ice twice.
Kassian was given two minor penalties for roughing, as well as a misconduct. Tkachuk was not penalized.
"If he doesn't want to get hit, then stay off the tracks,'' Tkachuk said after the game. "I got him three times there. You'd think he'd learn after the first one. If he wants to react like that, we'll take the power play, we'll take the game winner and we'll move on in first place.''
Kassian called the hits "targeted'' and was unhappy Tkachuk didn't respond with fists of his own.
"You don't let people take advantage of you no matter what the situation is,'' Kassian said, defending his actions.
The Flames won the game 4-3, scoring the decisive goal on the power play as Kassian served the second of his roughing minors.
The Oilers next play the Nashville Predators on Tuesday at 9 p.m. ET on ESPN+.
The Associated Press contributed to this report.