The Third Division Fifers were given a lesson in finishing by their Scottish Premier League opponents, who built up a two-goal interval lead before stepping up a gear in the second half.
Daly had threatened twice in the early stages before Cowdenbeath hit back with a 22-yard Jay Shields shot and a Paul McQuade effort that carried narrowly over.
But United were soon back on the attack, and they notched their opening goal in the 30th minute when Daly nipped in front of David Hay to head home a Craig Conway corner from close range.
Then, five minutes from the interval, United struck with their second goal. This time their marksman was David Goodwillie, who pounced to shoot home from eight yards following a Conway cross.
United virtually wrapped up the match as a contest with their third goal in the 49th minute. Goodwillie burst down the right and cut the ball back for Daly to fire a first-time right-foot shot past Hay from 14 yards.
Goodwillie got his second goal of the night to make it 4-0 in the 61st minute. He picked up a loose clearance 30 yards from goal and marched forward before unleashing a 22-yard drive that beat Hay at the far post.
Cowdenbeath grabbed a consolation goal in the 74th minute through substitute John Dempster, who shot home from eight yards from a McQuade cross.
But United restored their four-goal advantage, bringing the score to 5-1, in the 81st minute, with Daly again the marksman.
He fired low into the net from nine yards to complete his hat-trick and the rout.