Championship Derby were second best to the U's all afternoon and can have no complaints with this result.
Remarkably, this was Colchester's 18th win from their last 20 games. They have only lost one of their last 21 fixtures.
Danns broke a deadlock just before half-time to put the League One hosts in control.
Chris Iwelumo hooked on a long throw by John White and Danns slid home the loose ball, via the far post.
It was Danns' 12th goal of the season and there was more to come as the former Blackburn midfielder doubled the lead in the 52nd minute with his 13th of the campaign.
It was another long throw routine. Greg Halford's throw caused problems in the Derby box and although Richard Garcia had his shot blocked by defender Andrew Davies, the alert Danns was able to fire home from eight yards out.
Derby had been walloped 6-1 at Coventry the previous weekend and they must have thought that they were in for another hiding when Garcia added a third goal on the hour mark.
Garcia met Halford's cross with a downward header that keeper Lee Camp managed to block, but not hold on to and Garcia reacted quickly to poke home from close in.
It was Australian attacker Garcia's fourth goal in the last three matches and it meant there was no way back for woeful Derby.
The visitors did grab a consolation with 11 minutes remaining they were awarded a penalty for a push by Halford on substitute Lee Holmes and up stepped Tommy Smith to ram home the spot-kick.
But it was too little to late for Derby, as Colchester keep marching on. They're in the thick of the League One promotion race and are still going strong in both the LDV Vans Trophy and now the FA Cup.