Markstrom was the busier of the two goaltenders in the first period and saved his best work for a Calgary penalty kill in the later stages of the frame.
The Flames puck-stopper denied the Kings on a pair of one-timers, first on an Adrian Kempe slot shot, then off Anze Kopitar's effort from the left circle.
Los Angeles reclaimed the lead one second after their man-advantage expired, though, when Pierre-Luc Dubois redirected a point shot past Markstrom for his sixth goal of the campaign.
The Flames pressed to equalize before the first period was through, coming close on a speedy rush from Nazem Kadri that also produced a rebound opportunity from Martin Pospisil, but the Kings retained a 2-1 lead at the break.
Los Angeles outshot Calgary 13-7 in the opening frame.
The Flames ability to score shorthanded goals has been a talking point all season long, and again, the duo of Coleman and Sharangovich made good on an opportunity after Coleman stripped Kings defenceman Jordan Spence in the neutral zone.
He dished to Sharangovich, who floated a return feed back across the low slot for Coleman to bang into the net from just outside the blue paint 4:01 into the middle stanza.
The marker was Calgary's league-leading ninth shorthanded goal of the season, and sixth in December; Coleman has accounted for four of those tallies this month alone.