It was the Flames who got things started, jumping out to an early 2-0 lead.
Tkachuk slammed the puck home on the powerplay while Adrian Kempe sat in the box for interference. Tkachuk received a pass from Mikael Backlund behind the net, brought it out in front, and whacked away at it until it slipped past Jonathan Quick and in.
Frolik added to the lead later in the first, courtesy of an amazing Johnny Gaudreau assist. Gaudreau brought the puck up the ice, dangling through Kings players before dishing off to Frolik alone in the slot - right through Drew Doughty's legs - setting Frolik up for the easy tap-in.
The Kings, however, started coming back in the second period. Anze Kopitar ended Mike Smith's shutout streak at 139:50 with a shot that pinged off the far post and in.
Smith had a number of big saves prior to the goal, including a goal-line save, and stoned Kopitar earlier in the game when he came barrelling in on him.
"I think since the first game we've played a lot better hockey," Smith said. "We've done a lot of good things in games, so we continue to build on that, and learn from the mistakes that we're making in games, and we'll keep improving and pushing along."
The Kings tied the game early in the third period, courtesy of Brown tipping a Doughty shot. Shortly after, Brown scored again off of another tip-in, this time on Derek Forbort's shot.
With about nine minutes to go in the third Tkachuk tied the game up with his second of the night, beating Quick with a quick shot.