Trailing 2-0, the Flames went on a powerplay with just over five minutes left in the third period and pulled Markstrom for a 6-on-4 advantage but couldn't find twine.
They kept him on the bench and with 2:36 left to go and Michael Stone scored on a point blast while 6-on-5.
The Flames swarmed the net from there out looking for the equalizer before Columbus got an empty-netter with 23 seconds to go to ice it.
Earlier in the final frame, it appeared the Flames had scored after a pile up in the crease but after review the ref said the whistle went before the puck crossed the line.
Calgary had five powerplays in the contest but couldn't convert, while their PK went a perfect 7-for-7.
The game marked the first time the Flames had faced former teammate Johnny Gaudreau, who left via free agency in the summer.
Radim Zohorna played his first game of the season for the Flames, slotting in on the fourth line. Fellow Calgary Wranglers AHL call-up Matthew Phillips did not dress in the game.
Joonas Korpisalo made a big stop on Nazem Kadri less than a minute into the game, the puck soon finding its way onto the stick of Patrik Laine who had a breakaway and beat Markstrom with a wrister over his left pad and under his glove at 1:02.
The Flames got the first powerplay of the game and it was again Kadri with a great look, denied on a one-timer as he finished off a quick passing play.
Calgary went 0-2 on the man-up in the period.
Markstrom made a 10-bell, highlight-reel-worthy save on a 2-on-1 later in the frame, Gaudreau passing across to Laine but the Calgary 'tender stacked his pads to absolutely rob him.
Then after a lengthy Flames possession in the Jackets zone, Yegor Chinakhov was able to steal the puck up high and had a 2-on-0 with Laine, electing to keep and fire but Markstrom stood tall.
Korpisalo did not return for the second period, out with a lower-body injury, with Elvis Merzlikins replacing him between the pipes.
The homeside got their second goal of the night at 2:52 of the second period following a turnover in the Calgary zone, Eric Robinson going high glove side past Markstrom on a partial breakaway.
