Airdrie, beaten 3-0 by Rangers in the Scottish Cup earlier this month, produced a battling performance but were undone by second-half goals from Jon Daly and Lee McCulloch.
Rangers dominated from the start with Airdrie keeper Andrew Duncan saving Daly's header before Daly, Nicky Clark and Lee Wallace all fired wide.
The visitors had a rare effort at goal as Martin Hardie's free-kick sailed over the bar, but the hosts were quickly back on the front foot as Duncan made a point-blank save to foil Clark.
Wallace then blazed over and Bilel Mohsni shot straight at Duncan before shooting wide as the teams went into the break all-square.
However it took Rangers only 38 seconds to score after the restart when Arnold Peralta's right-wing cross was flicked on by Clark for Daly to head home his 16th goal of the season at the far post.
Clark was then twice foiled by Duncan before he crashed a header against the crossbar, while David Templeton's long-range drive also tested Duncan.
McCulloch made it 2-0 from the penalty spot, rocketing home from 12 yards after Templeton had been felled in the area by Gregor Buchanan.
Nathan Blockley lifted a shot over the bar as Airdrie attempted to pull a goal back but Rangers held firm to take their points haul to 36 for the season, which puts them 16 points clear at the summit.