Steve Duchesne slipped and Andrew Cassels scored.
"Before I knew it, I was in all alone and I went five-hole," said Cassels after the Flames won for the fourth time in five games.
On the play, Kings defenseman Duchesne lost his balance at his own blue line, allowing Cassels to break in alone on Bach.
The Flames had trailed throughout the game 3-0 midway through the second period, and 4-2 with less than 10 minutes remaining in the third.
"We stuck to what we wanted to do, we kept working hard and tried not to open it up too much," Cassels said.
The Flames got third-period goals from Cory Stillman at 10:16 and Derek Morris at 17:32 to tie the game.
"It was a complete collapse, we gave them the game," Kings coach Larry Robinson said. "You don't get these points back."
Theoren Fleury and Valeri Bure also scored for the Flames.
Fleury's 10th goal of the season moved him into a tie with Edmonton's Bill Guerin for the league lead.
Luc Robitaille, Glen Murray, Olli Jokinen, and Vladidmir Tsyplakov each had a goal and an assist for the Kings.
It was the first time the Kings had blown a three-goal lead since an 8-6 loss Nov. 30, 1993, against the Winnipeg Jets.
Until the Flames launched the late comeback, the night belonged to the streaking Kings line of Robitaille, Murray and Finnish rookie Jokinen whose goal was the first of his NHL career.
The three combined for six points, giving the line 19 points over the last four games. Murray and Robitaille have scored in each of those four games.
The loss spoiled the first NHL start for Bach, who has now lost both of his appearances. The 25-year-old, who began the year with Utah of the IHL, took the loss in relief of Manny Legace on Oct. 23 in Tampa Bay when he yielded two goals in a 3-2 defeat to the Lightning.
Fellow rookie Jean-Sebastien Giguere, meanwhile, has won his first two starts for the Flames.
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