In a wild third period, the Flames took the lead twice only to see the Blues come back to tie it each time. Calgary finally went in front for good when Versteeg's shot off the wing beat goalie Jake Allen.
Sam Bennett scored his first of the season for Calgary, and Micheal Ferland got his fourth goal in four games. Johnny Gaudreau and Michael Frolik also scored as the Flames finished 5-2-0 on their longest homestand of the season.
Gaudreau had two points to extend his point streak to seven games (five goals, seven assists).
Vladimir Tarasenko scored twice for St. Louis, and Jaden Schwartz and Alexander Steen also scored.
Bennett put the Flames in front 3-2 to open the third-period barrage when his backhand of Jankowski's shot slipped through Allen's pads.
Steen tied it at 11:46 and then Ferland's power-play goal restored Calgary's one-goal lead at 12:31. But 12 seconds later, Tarasenko one-timed a pass from Schwartz to tie it again.
Mike Smith, who has started 16 of Calgary's 17 games this season, had to leave after the first period with an undisclosed injury. Eddie Lack played the final 40 minutes, stopping 13 of 15 shots for his first win with the Flames.
Allen stopped 30 of 36 shots.
St. Louis opened the scoring 3:32 in on its first shot. Colton Parayko crossed the blue line and dropped the puck to Tarasenko, who beat Smith from 40 feet on a high wrist shot over his blocker.
Jankowski scored the next two goals to give Calgary its first lead of the night. With the teams playing four skaters aside, he hammered a slap shot over Allen's glove at 4:54. Jankowski then took a slick pass from Jaromir Jagr and scored on deke at 13:45.
