Between them, the League Two outfits have seen off the challenges of Premier League trio Norwich City, Crystal Palace and Tottenham Hotspur respectively.
Having finished in the bottom half of the League Two standings in the last four seasons, this campaign for Crawley Town was again supposed to be focused on attempting to avoid any kind of relegation battle.
However, victories over Norwich and Stoke City have put the fourth-tier side in contention for a spot in the last eight of this competition for the first time in their history.
That said, since the penalty-shootout success over Stoke, just one win has been recorded in seven outings, and Crawley head into this tie having suffered a 4-0 defeat at home to Swindon Town at the weekend.
Meanwhile, Colchester got back onto the right track on Saturday by recording a 3-1 success over Newport County - an impressive scalp given the defensive record of their opponents.
That result marked the club's first league success since October 5, moving the U's up to ninth spot in the table and just four points off the playoffs.
Manager John McGreal will now feel that his squad are in a positive frame of mind ahead of such an important fixture as they attempt to build on two penalty-shootout triumphs over Premier League opposition.
Colchester are bidding to reach the last eight of the League Cup for the first time since the 1974-75 season.
Crawley Town form: LLWLDL
Colchester United form: WDLLDW
While Cioffi will name a strong team for this contest, the Italian will almost certainly make several changes after the poor performance at the weekend.
Beryly Lubala is available again after serving a one-match suspension for collecting five yellow cards.
Colchester boss McGreal could name the same starting lineup which began the encounter with Newport.
Crawley Town possible starting lineup: Morris; Sesay, Tunnicliffe, Dallison, Doherty; Grego-Cox, Camara, Ferguson, Nathaniel-George; Enigbokan-Bloomfield, Nadesan
Colchester United possible starting lineup: Gerken; Jackson, Eastman, Prosser, Bramall; Stevenson, Comley; Senior, Poku, Nouble; Norris
We say: Crawley Town 1-2 Colchester United
There will inevitably be a lot of tension and nerves throughout this fixture. While Crawley have home advantage, it may be to their detriment, and we feel that Colchester will have enough quality to edge through.