Daly headed home in the 36th minute and soon fired home to give United a well-deserved and comfortable half-time lead against an under-strength Motherwell.
The Irishman took advantage of more slack Motherwell defending to put the game out of the reach four minutes into the second half and substitute Andis Shala claimed a late fourth.
The victory put United five points behind Hearts with both sides now facing the Old Firm before meeting at Tannadice on the final day.
Peter Houston's men, who will be looking to repeat last month's Ibrox win on Tuesday, also closed their goal-difference deficit to six after being earlier boosted by Hearts' 4-0 defeat by Rangers.
Motherwell had beaten United four times already this season but manager Stuart McCall rested Stevie Hammell, Keith Lasley and John Sutton with the Scottish Cup final against Celtic in mind and captain Stephen Craigan started on the bench.
Tom Hateley, Shaun Hutchinson, Ross Forbes and Stuart Carswell were drafted in while Chris Humphrey returned from a dead leg, but Well have now conceded 12 goals in three games since reaching the final.
Motherwell started with five in midfield and struggled to support Francis Jeffers in the first half. United had the edge from the start and Johnny Russell came close to a glorious goal in the 16th minute when he met Daly's cross on the volley from 18 yards out, but the shot whistled a yard over the top corner.
Darren Randolph was comfortably behind headers from Keith Watson and Daly before Gavin Gunning got back to block well from David Goodwillie after the Motherwell defence had been caught square.
Randolph then parried Morgaro Gomis' curling effort after good work from Russell and United winger Craig Conway shot over after being afforded yards of space on the right.
Motherwell appeared to have weathered the storm but Randolph soon made a rare error.
Dixon was given the chance to flight the ball in after Forbes had been booked for a foul on Gomis in midfield and Daly aimed a header which was far from emphatic but squeezed in between Randolph and his post.
Daly grabbed his second in the 43rd minute. Garry Kenneth's measured pass found the Irishman in space just inside the box and he turned away from Hutchinson before firing into the bottom corner.
Centre-backs Hutchinson and Gunning were then involved in a heated discussion over how Daly was afforded such room, but Gunning was unquestionably to blame when Daly completed his hat-trick. The on-loan Blackburn defender misjudged Dixon's cross and saw it float over his head straight to Daly, who chested down and fired into the corner from 12 yards.
Motherwell soon brought on striker Gary Smith for midfielder Forbes and both he and Carswell threatened from Hateley corners without forcing Dusan Pernis into action.
But Daly was still getting chances. The former Stockport striker was too high with a chip from 25 yards after Hutchinson had misjudged a long ball, and then headed against the outside of the post from a tight angle following Conway's deep cross.
Pernis made his first save in the 61st minute, holding Humphrey's low drive at the second attempt. Motherwell brought on Craigan for Maurice Ross and they improved considerably in possession, with Jeffers curling just wide from the edge of the box.
But United regained control and Randolph tipped over Goodwillie's header before being beaten again in the 88th minute.
Watson scuffed a shot towards goal following Dixon's corner and the ball rolled into the corner as sub Andis Shala claimed the final touch from close range, although it was not clear whether he made contact.