Colchester had conceded seven goals in their last two games and the result was never in doubt once Garry Monk had headed his side into the lead.
Darren Pratley converted Cedric Van der Gun's cross on 35 minutes and Van der Gun made sure of Swansea's progress after finishing from close range on 68 minutes.
Scott Sinclair put the icing on the cake in the 82nd minute for Swansea, who will be looking for a high-profile clash in the fourth round.
Colchester were thrashed 7-0 by Preston at the same stage of the competition last season, and rarely threatened the Swans goal.
Swansea manager Brendan Rodgers made five changes to the team which lost 2-1 to Leicester on Monday, with Luke Moore - who only completed a permanent move from West Brom - and Daniel Alfei making their debuts to help the hosts to romp home with ease.