Ryan France broke the deadlock in the 11th minute by putting the finishing touch to a superb breakaway. A Colchester free-kick broke down in the Hull penalty area and, suddenly the visitors were on the attack with Elliott racing down the left-wing. Elliott spotted France in acres of space, and Hull's midfielder advanced a few yards before beating keeper Aidan Davison with a low shot from the edge of the box for his first league goal of the season.
The Tigers doubled their tally in the 50th minute when Elliott received a pass from Andy Dawson and let fly with a shot that bounced over the outstretched body of keeper Davison and into the far corner of the net. The ball did hit a bobble but it was still a bad error from Davison. It was Elliott's 16th goal of the season.
Colchester certainly missed the services of their leading scorer Craig Fagan, who was serving a one-match suspension for being sent off against Barnsley in midweek.
As a result the Essex side lacked much of a goal threat, although this changed when substitute Gareth Williams replaced Jamie Cade in the 69th minute.
Williams pulled the goal back within four minutes of his introduction. He had the simplest of tasks when diverting the ball home from Greg Halford's excellent cross from the right wing. It was a mere tap-in for Williams, clocking up his third goal of the season.
But Colchester could not find an equaliser during the closing minutes and so have now lost four of their last five league games at Layer Road.
Indeed, Phil Parkinson's men have only gathered one point from a possible 15 at Layer Road since they beat Port Vale on October 2.
It was an improved performance from Colchester and they could point to two earlier efforts which went begging. Both Cade and Joe Keith lifted shots over the top from good positions early in the second half.