Collins opened the scoring in the 20th minute and doubled his tally nine minutes later before securing the match ball midway through the second half.
Kiernan Dewsbury-Hall sent an early volley way over the bar for the hosts as Preston had the better of the opening 15 minutes.
Alan Browne fired wide from a corner routine before Luton were ahead when Pelly-Ruddock Mpanzu's wonderful cross-field ball was chested down by Collins to go one-one with keeper Declan Rudd and slide into the bottom corner.
Mpanzu just couldn't reach Moncur's cross to add a quickfire second but Luton were 2-0 up after 29 minutes.
This time Moncur's delivery was cleared as far as Glen Rea, who knocked it back in for Collins to nod home from a few yards and double his side's advantage from close range.
Town were almost hit on the break after 37 minutes, Browne side-footing harmlessly over from 20 yards after a quickfire counter.
But they were soon back at it, Moncur's fizzer going just over the top and Harry Cornick was unable to divert Matty Pearson's cross on target.
In the second period, Moncur looked for a third, his effort from the edge of the box easy for Rudd, as an unimpressed visitors boss Alex Neil made all five of his changes by the hour mark.
Mpanzu should really have made it 3-0 as Preston lost possession when being pressed by the hosts. The ball fell to him 20 yards out but, with Rudd out of position, he could only slam over the top.
Collins was denied a perfect hat-trick, his left footed volley hitting a defender, but he did have a treble after 66 minutes.
Found by Moncur after another error at the back, the leading scorer transferred the ball on to his right foot and from just outside the box arrowed his shot into the bottom corner.
Still Luton looked to increase their margin of victory late on, Rea shooting at Rudd from 25 yards while sub Jordan Clark sent a half-volley into the stands.
Tom Lockyer's header then fell inches wide with five to go on a marvellous afternoon for the Hatters.