Daly and another summer arrival Nicky Law were joined on the score sheet by Lewis Macleod, Andy Little and Robbie Crawford at the Excelsior Stadium.
Rangers opened the scoring when Macleod collected Crawford's pass and sent a low drive beyond the grasp of the Airdrie goalkeeper after 18 minutes.
And Little (36) doubled the lead when he met a Daly header and crashed home from six yards, while Crawford drilled home at the back post to finish the contest just after the break.
Daly netted his first on 64 minutes with a header from close range when a Crawford shot deflected into his path.
Three minutes later when a Little cross was flicked in by Law, and Daly completed the scoring with a low drive into the corner.