Calgary (12-10-2) has reeled off seven straight wins on home ice to move into a tie with the Colorado Avalanche for eighth spot in the Western Conference.
Ron Hainsey scored the lone goal for the Blue Jackets (6-16-2), who have lost five in a row on the road and have just one win in their last 11 overall (1-9-1). Ken Hitchcock dropped to 1-3-0 since taking over head coaching duties on Nov. 22.
Trailing 1-0 entering the third, Iginla scored his team-leading 13th goal at 4:10. Robyn Regehr's shot from the blue-line hit Iginla in the leg as he screened goaltender Pascal Leclaire. The puck dropped down at his feet and he knocked it past Leclaire to tie the game.
With the sell-out crowd of 19,289 at the Pengrowth Saddledome still buzzing, Kobasew put the Flames into the lead at 6:38 with his first goal in 16 games. His goal came on a bizarre sequence that began when Kobasew's close-in shot hit the goal post, resulting in the goal light coming on by mistake.
As the puck lay in the crease, Leclaire knocked it away with his blocker. It ended up back on the stick of Kobasew, who found the top corner with a shot from a sharp angle.
Until the Flames rallied in the third period, Leclaire had kept them at bay with some sensational goaltending.
In one stretch in the second period, he came across the net to deny Marcus Nilson's shot from close in. Shortly after, Leclaire jabbed out his blocker to deflect away a dangerous slapshot from Kristian Huselius.
Leclaire was also the benefactor of some good luck. In the opening minute of the third period, Dion Phaneuf had Leclaire beaten on a close-in shot but blasted a shot off the crossbar.
Columbus opened the scoring with a power-play goal in the closing moments of the first period. A bad line change by the Flames enabled Alexander Svitov to dangerously dash into the Calgary zone. He left the puck for Anders Eriksson, who neatly faked a shot and dropped the puck back to Hainsey at the blue-line, who quickly fired a wrist shot past a screened Miikka Kiprusoff.
The goal came late on the Blue Jackets' first power-play opportunity of the night and was a welcome sight, with the Blue Jackets mired in a 4-for-52 slump with the extra man over the previous nine games.
However, Columbus was unable to connect on any of its final four man advantages - including two power-play opportunities in the third after they had fallen behind.
Calgary outshot Columbus 31-19.
Notes: Columbus LW Fredrik Modin (groin) missed his second game. He is recovering back in Columbus but could be ready next Tuesday when the Blue Jackets play in Colorado. . . . Iginla is one assist away from 300 for his career and two goals away from 300. . . . It was just the sixth time Columbus has scored the game's first goal (4-1-1) and fifth time they've led after the first period (3-1-1). . . . Calgary doesn't play again until Tuesday night when Carolina comes to town. The Flames will not have three days off in a row again until the all-star break in late-January.