Nick Foligno also scored for Columbus (8-11-3). The Blue Jackets are 2-1-0 with two stops left on a five-game road trip. They play in Vancouver on Friday.
Joe Colborne scored for Calgary (7-11-4), which is winless in its last six (0-5-1) at the Scotiabank Saddledome.
The Flames were coming off an emotional 5-4 shootout victory in Winnipeg on Monday night. They were trying to win two games in a row for the first time in over five weeks.
Coming off a disastrous 7-0 shellacking in Edmonton on Tuesday night, Columbus was a lot tighter defensively Wednesday, limiting the Flames scoring chances until Calgary tied the game 3:28 into the third period.
Kris Russell found David Jones near centre with a long breakout pass and as the Blue Jackets all flocked to him, Jones neatly left the puck for Colborne. He blew past a flat-footed Jack Johnson, and on a breakaway tucked a backhand over the shoulder of Bobrovsky.
Bobrovsky bounced back with a better game after being pulled against the Oilers midway through the second period after the fourth goal.
Bobrovsky wasn't overly busy but he made the stops he needed to and finished with 23 saves. After winning the Vezina Trophy last year as the NHL's best goalie, Bobrovsky has not had nearly the same success this season with a 7-9-2 record.
Berra made his eighth start in his last nine games for the Flames. He made 16 stops to fall to 2-5-1.
Columbus opened the scoring on the only goal of the first period.
Foligno's slapshot deflected off the leg of Flames defenceman TJ Brodie, the sudden change in direction sending it into the top corner behind Berra.
Just a couple minutes earlier on a Columbus power play, Berra had turned in a highlight-reel save to keep the game scoreless.
Johnson looked like he had all sorts of open net to shoot at but Berra came across and, using his entire six-foot-four frame, stretched out and spectacularly kicked the puck out of the air like a bicycle kick in soccer.
Before the game had ended, the video of it was already up on the NHL's website with the headline "Save of the year?"
That would be the highlight of the what was otherwise a very lacklustre opening 40 minutes.
Notes: The Blue Jackets were without Brandon Dubinsky, who suffered a bruised foot against Edmonton. Recently recalled Jack Skille took his spot ... Columbus LW Matt Calvert (lower body) is back practising and he could return Friday. He's missed 19 games ... Bobrovsky has given up four-or-more goals six times this season. That happened only five times all of last year ... Calgary is 6-3-4 in one-goal games.