In-form Nacer Chadli fired us ahead in the first half, before Eric Dier's deflected shot doubled our advantage on 64 minutes.
Chadli then netted his second of the afternoon and our third, a Ben Davies own goal gave Colchester a goal back but Tom Carroll quickly restored our three-goal cushion to see us safely through into the fifth round, the draw for which takes place on Sunday.
Colchester (4-4-2): Kean, Brindley, Eastman (Briggs 21), Wynter (Kent 6), Vincent-Young; Massey, Gilbey, Garvan, Moncur; Ambrose (Sordell 61), Porter. Substitutes (not used): Parish, Edwards, Lee, Bonne.
Spurs (4-2-3-1): Vorm; Trippier, Dier, Wimmer, Davies; Bentaleb, Carroll; Lamela (Dembele 55), Eriksen (Onomah 77), Chadli; Kane (c) (Son 68). Substitutes (not used): Lloris, Alderweireld, Walker, Alli.
Goals: Colchester – Davies (OG) 80. Spurs – Chadli 27, 78, Dier 64, Carroll 82.
Referee: Michael Oliver.