The hosts had 14 efforts at goal in the first half, but the best chance fell to Nicky Clark after 30 minutes when Lee Wallace shot came off a defender into his path; however, his close-range attempt was blocked by keeper Andrew Duncan.
Despite going in level at the break, Rangers took only 38 seconds of the second period to edge in front thanks to Daly, who headed Arnold Peralta's cross beyond Duncan.
The home side's lead doubled just after the hour mark from the penalty spot. David Templeton's run was brought to an abrupt halt in the penalty area and Lee McCulloch made no mistake from the spot.
Rangers held on to their lead and the result means that they lead Scottish League One by 14 points.
Airdrie will be happy to see the back of Glasgow side, having lost 3-0 at Ibrox in the Scottish Cup last week.