The runaway League One leaders were held goalless until half-time but Gary Thom’s own goal turned the tide and Daly’s 15-minute treble sealed the result.
Ally McCoist’s side are 11 points clear of both Ayr United and Dunfermline, while the Glasgow side have a positive goal difference of 37.
Bilel Mohsni went closest for Rangers in the opening period while captain Craig Johnstone threatened for the home side.
Ian Black saw his effort chalked off but when Thom (49) diverted Lee Wallace’s cross past Greg Paterson early in the second half, the pattern was set for the rest of the contest.
Daly met Arnold Peralta’s cross to find the bottom corner (52) and before the home side could regroup, Nicky Clark set up the striker’s second goal, another close-range header (57).
The scoring was not over there, and Lewis Macleod was afforded time and space to tee up Daly for his hat-trick, executed with a crisp right-foot finish (66).
Rangers goalkeeper Cammy Bell stood tall to deny Scott McBride a late consolation.