Dustin Wolf made 20 saves for the surging Flames. They have won eight of their last 12 games, with Wolf winning his last four starts.
Frost capped a 3-on-1 break from Jonathan Huberdeau at 1:06 of overtime for his eighth goal of the season, and Calgary took advantage of the reprieve after Anze Kopitar's apparent winner 33 seconds into the extra session was overturned for a kick after a video review.
Adrian Kempe scored for the Kings and Darcy Kemper made 36 saves. Los Angeles had its 14th game decided by overtime or penalty shootout this season in its 21 games with a goal.
The Kings got off to a strong start, with Kempe scoring his fourth goal in his last seven games with one midway through the first period. He has two goals and five points during the four-game streak.
But the Flames responded with a dominant second period, posting a 17-4 shot advantage, and finally broke through when Coleman deflected a Kevin Fiala pass and raced the other way, breaking away before knocking down a wrist shot from the slot. It was Coleman's third shorthanded goal of the season and Calgary's fifth.
Flames: Visit the San Jose Sharks on Tuesday.
Kings: Visit the Dallas Stars on Monday.
