The in-form Belgian got himself on the scoresheet for the third match in succession and the result was rarely in doubt against a spirited U's side who refused to throw in the towel in our first competitive visit to the Weston Homes Community Stadium.
After Chadli's opener, Eric Dier added the second goal via a deflection during the home side's best spell in the second half.
Chadli then scored again and just two minutes after Ben Davies inadvertently turned into his own net, Tom Carroll converted Chadli's cross from close range for the final 4-1 scoreline.
Harry Kane took over the captain's armband for the fourth round trip to Essex while Kevin Wimmer was partnered by Eric Dier at centre-back. In front of them, Nabil Bentaleb and Carroll came in to anchor the midfield.
It was chilly and blustery and a sell-out crowd greeted both sides, with the League One outfit intent on causing an upset.
We immediately came out of the blocks as Kieran Trippier beat his man and sent a dangerous cross in for Chadli within a minute, but he failed to hit the target with his header.
There followed a lengthy delay as Alex Wynter was stretchered off after what looked like a clash of heads with Tom Eastman. We wish him a speedy recovery.
Trippier was finding acres of space on the right upon the resumption and had another dangerous cross scrambled clear before Christian Eriksen brought the best out of Jake Kean in the Colchester goal.
It was one-way traffic inside the opening 10 minutes but desperate defending and Kean kept the scores level. The home side were down to 10 men for a long time as Eastman received extensive treatment for the clash with Wynter before returning with a fresh shirt and bandaged head.
Erik Lamela let fly from distance and was a whisker away when his shot hit the bottom of the post, while Kane was next to go close when he found the side-netting from another Trippier cross.
Eastman eventually was unable to continue and was replaced midway through the half before a scare for us when Michel Vorm scrambled off his line to clear a through ball and almost handled outside of his box.
Eriksen had our best chance with 25 minutes gone when Kane put him through on the break but, being forced wide, he blasted over.
Just seconds later, though, we had the lead. Lamela stabbed the ball into the path of Chadli who curled past Kean with a brilliant finish into the top corner.
Colchester responded well to the goal but Kean kept them in it on the half-hour mark with a brilliant point-blank save from a Kane header.
It was a more even affair for the rest of the half and the home side would have been pleased heading in at the interval to still be in the game.
There were no changes at half-time but Lamela should have put us 2-0 up within two minutes of the restart when he controlled a Kane pass well but prodded a shot wide on the angle.
Colchester's Darren Ambrose had a decent effort deflected behind five minutes later after good work from George Moncur.
The home side had changed their style and were pressing further up the pitch which seemed to suit them more and it meant there was a more even balance to the game in the second half.
Chadli had a chance to seal it on the hour mark when Kane squared the ball to him but he rattled the bar from close range.
We would not have to wait long, however, for that second goal. In possession but with few options ahead of him, Dier strolled into the Colchester half, took aim from distance and saw his shot take a wicked deflection past the helpless Kean.
The goal took the sting out of the game somewhat and with 20 minutes to go, Kane made way for Heung-Min Son with Mousa Dembele taking over the armband after signing his new contract on Friday.
Son had a shot well saved soon afterwards but it was the home side who had the clearest opening of the game when Marvin Sordell robbed us of possession and went through on goal but hit the post with just Vorm to beat.
It was 3-0 with just over 10 minutes to go, though. Trippier had sent a deluge of dangerous balls in throughout the game and finally one got the finish it deserved when Chadli headed home.
There was a twist in the tale two minutes later when a shot from Sordell hit our post and rebounded back against Davies and into the net, but it was goals galore at that stage as we went straight back up the other end with Carroll delicately turning in a Chadli cross via the crossbar.
That rounded off the scoring as we await the draw for the fifth round 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.