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 today - and Daniel Alfei making their debuts.
U's boss John Ward described the 4-2 defeat to Leyton Orient as the worst performance under his tenure, but he kept faith in the majority of the side as David Perkins replaced the injured Ashley Vincent and Kemal Izzet returned from suspension to oust Lloyd James, who dropped to the bench.
Ward's players more than justified their selection in the opening exchanges as they stifled the opposition, although they failed to create any meaningful openings of their own.
However, they found themselves a goal down when Monk put the hosts in front after 25 minutes.
Mark Gower's right-wing cross found the unmarked defender, who had stayed up front from a corner, at the back post and he headed past Ben Williams.
That was Swansea's first effort on goal and it served to highlight Colchester's fragility in defence.
Their woes increased when Pratley doubled the Welsh side's lead 10 minutes later for his sixth goal of the season.
The midfielder had already struck narrowly wide from the edge of the area before he latched onto Van der Gun's cross from the right and coolly slotted home from 12 yards.
Matt Heath saw his shot go just wide of the right-hand post with a shot from the edge of the area and David Mooney forced a fine save from Yves Ma-Kalambay as the visitors made a bright start to the second half.
They could not maintain their tempo however and Van der Gun put Swansea three goals to the good in the 68th minute.
Sinclair made a fine run down the left before he laid the ball across the six-yard area for Van der Gun to tap in.
The creator turned goalscorer eight minutes from time when Joe Allen's through ball found Sinclair and he calmly finished past Williams to seal the rout.