Chris Brown and Chris Sedgwick had given Preston a 2-0 lead at half-time on a miserable afternoon for Adrian Boothroyd's high-flying League One outfit.
Preston interim boss Kelly had Ross Wallace back from suspension and the Scottish winger was at the heart of much of the home side's best work in the opening exchanges, although Preston had an early scare when Simon Hackney flighted a dangerous ball into the penalty area only for Phil Ifil to take an air-shot at the back post.
In the ninth minute, Carter produced a rasping 25-yard drive which Williams could only parry as far as Neill Collins, but the Lilywhites defender volleyed wide when well placed.
Collins could breathe a sigh of relief four minutes later when North End took the lead.
Brown rose highest to nod home Wallace's inswinging corner and register his eighth goal of the season and fifth in cup competitions.
Brown and Parkin both spurned chances to extend the lead before the second goal arrived after 27 minutes.
Sedgwick was set up by the impressive Brown before unleashing a shot on the angle which took a wicked deflection off Paul Reid and looped over Williams.
Five minutes before the interval Colchester had a chance to get back in the game when the ball broke to Steven Gillespie, but the forward miscued with the goal gaping.
Preston moved to the other end of the pitch immediately and Wallace played in Parkin behind the visitors' defence but the bustling frontman shot straight at Williams.
He was to make amends with style in the opening minutes of the second half.
Less than 90 seconds after the restart Callum Davidson launched the ball towards the Colchester area where Brown flicked the ball into his strike partner's path.
Parkin then spun and smashed a low shot beyond Williams' grasp.
The former Stoke man had his second two minutes later when he shrugged off the attentions of the Colchester back line to collect a long ball and superbly lob Williams.
The beleaguered Colchester goalkeeper saw his afternoon get even worse in the 52nd minute when Brown completed some neat link-up play on the edge of the penalty area and curled a shot towards the bottom corner of the goal.
His shot bounced back off the foot of the post, hit the hapless Williams on the back of the head before resting in the back of the net.
Carter made it six in the 64th minute when he collected a loose ball in midfield and cut effortlessly through the visitors' defence before slotting home.
Parkin completed his hat-trick from the penalty spot with 18 minutes remaining after he was brought down by Magnus Okuonghae.