Iginla had missed the last 11 games with a knee injury. The Flames were 7-2-2 in the superstar winger's absence.
Kristian Huselius and defenceman Robyn Regehr also had a goal and two assists for the Flames. The goal was Regehr's first in 62 games.
It's just the second time in his seven-year career that Regehr has had three points in a game. The last time was on Feb. 6, 2006 in San Jose when he recorded three assists during a 4-3 win over the Sharks.
Mark Giordano had a goal and an assist, while Daymond Langkow and Rhett Warrener also scored as the Flames (28-17-6) won their second straight game and sixth consecutive on home ice.
Rostislav Klesla and Jason Chimera scored for the Blue Jackets (21-27-5), who lost their second straight game after dropping a 5-2 decision in Edmonton to the Oilers two nights earlier.
After killing off two early penalties, the Flames scored goals just 19 seconds apart mid way through the first to take a 2-0 lead.
Iginla opened the scoring on a power play as he converted a feed from centre Craig Conroy. The former linemates were reunited again for the first time since Calgary's run to the Stanley Cup finals in 2004.
On Calgary's next rush, Alex Tanguay skated behind the net and fed Regehr at the point, who blasted the puck into an empty net as Columbus defenceman Adam Foote collided with netminder Ty Conklin to take him out of the play.
Regehr then set up Giordano, who sent a wrist shot past Conklin for a power-play goal. Calgary registered three goals in the first period for the first time this season.
Langkow opened the scoring 30 seconds into the second when he one-timed a pass from Huselius past Conklin.
Klesla finally put Columbus on the scoreboard at 1:03 of the second as he swatted a puck past Calgary goalie Miikka Kiprusoff while falling to the ice in front of the net.
After Huselius finished off a pass from Iginla during another Flames man advantage, Chimera replied for Columbus just as a penalty to Calgary enforcer Eric Godard expired.
Warrener rounded out the scoring in the third during a two-man advantage for the Flames when his point shot was tipped past Columbus replacement goalie Tomas Popperle by Blue Jacket defenceman Anders Eriksson.
The Flames were a perfect 6-for-6 on the penalty kill and scored a season-high four power-play goals on 10 opportunities.
Kiprusoff made 20 saves in the Calgary net, while Conklin stopped 11 of the 16 shots he faced before being pulled in the second period in favour of Popperle, who blocked eight of the nine shots directed his way in his first-ever NHL game.
Notes: Defenceman Andrew Ference and forward Byron Ritchie were healthy scratches for Calgary, while defenceman Aaron Johnson (healthy scratch) and Nikolai Zherdev (flu-like symptoms) missed the game for Columbus. ... For the first time in nine games, the Flames outshot their opponent. Calgary has been outshot 11 times in the past 13 games, during which time they've recorded a 9-2-2 record.