Victory strengthened Hull's position in the promotion race and, with the addition of Fagan who is due to complete the deal on Monday, they should be even stronger.
A further boost for Hull was manager Peter Taylor agreeing to sign a two-year extension to his contract, and they celebrated with a fluid first-half display.
Cort grabbed the lead from the first corner of the match, taken by Andy Dawson, with a firm header into the corner.
Hull maintained the pressure with Stuart Elliott heading over the top and Stuart Green driving just wide before Barmby grabbed the second to virtually secure the points.
Goalkeeper Aidan Davison rushed to the edge of the area to block an Elliott attempt and the ball broke to Kevin Ellison who hit the bar from long range. The ball then fell to Barmby, who passed it into the net with the minimum of fuss.
The first Colchester threat came from Gavin Johnson whose header troubled Boaz Myhill, although the U's were unable to cash in on the goalkeeper's fumble.
Colchester reorganised in the second-half when Greg Halford moved into attack to replace the disappointing Guylain Ndumbu-Nsungu.
And the U's should have forced their way back only for Gareth Williams to slice wide from six yards.
The miss sparked more Hull pressure with Elliott feeding Ellison who had Davison at full stretch.
A goal hungry Elliott then sent an angled drive whistling over the top followed by a header just wide.
As time ran out Johnson tested Myhill with a powerful header from the edge of the area.