Moncur fired home from Chris Porter’s pass with eight minutes remaining to keep the U’s up on a dramatic afternoon at the Weston Homes Community Stadium.
Richard Brindley’s long-range effort was pushed around his near post by Preston goalkeeper Sam Johnstone.
And at the other end, Colchester keeper Sam Walker had to be alert to deny both John Welsh and Chris Humphrey.
The hosts had a great chance to go ahead in the 57th minute when Johnstone brought down Moncur in the area but Porter ballooned the resulting penalty way over the crossbar.
Jacob Murphy had a good opportunity to score when he raced onto Gavin Massey’s pass but he fired straight at Johnstone, as did Moncur shortly afterwards.
Walker pushed away Joe Garner’s fierce effort before Moncur slotted home from Porter’s pass, to keep Colchester up against all the odds and leave Preston in the play-offs.