The equalising goal was another spectacular strike from City's man of the match Dickson Etuhu.
Colchester made a lively start forcing two corners early on, but when the home side broke away Robert Earnshaw's shot was blocked.
Former Canary Cureton fired in a shot from long range and was only inches away from opening the scoring.
His next shot brought a smart save from Paul Gallacher before Robert Eagle's inswinging corner almost deceived Aidan Davison who scrambled it away at the last minute.
Chris Iwelumo was fortunate to only be shown a yellow card for a challenge which left Gallacher stretched out on the turf after 31 minutes.
In the dying minutes of the half Etuhu fired straight at Davison after a good passing move from Norwich.
At the other end, Gallacher did well to block a Cureton header with Gary Doherty clearing the loose ball.
The central defender was also on hand to deny Cureton a scoring chance a minute later.
Five minutes after the restart Eagle put in a low cross from the left but Earnshaw was unable to turn it goalwards.
The visitors went ahead soon after as Gallacher blocked Johnnie Jackson's shot but, when the ball was played back across goal, Cureton blasted a right-foot shot into the roof of the net from six yards.
Twenty minutes later Norwich drew level when Huckerby played the ball to Etuhu and his fierce right-foot shot from 25 yards beat Davison low to his left.
Six minutes later Dublin rose majestically to meet Huckerby's left-foot cross but his header cleared the bar.
In the dying seconds Dublin was fouled but Earnshaw's free-kick flew inches wide.