The Championship side, winners in 1927 and runners-up as recently as 2008, produced a professional performance against the League One strugglers, who sit second bottom of England's third tier.
A heavily deflected strike from Joe Ralls put Cardiff ahead in the 34th minute, with a Kadeem Harris effort and Kenwyne Jones' header effectively sealing progression prior to Freddie Sears' consolation for Colchester.
Elsewhere, Chesterfield will play Scunthorpe United in the third round on Tuesday after beating MK Dons 1-0 in a replayed second-round tie.
The two teams were ordered to face off again in the second round following the revelation that Chesterfield had fielded an ineligible player in the first tie, which Paul Cook's side won by the same scoreline.
A cool 43rd-minute finish from Gary Roberts gave the visitors victory over their League One rivals this time around, securing a trip to Glanford Park for Chesterfield.
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