The Swans booked their place in round four of the FA Cup with this win against Colchester.
It took some time for the hosts to get going but the deadlock was broken midway through the first-half when Garry Monk headed home from Mark Gower's cross.
The skipper was forced off within minutes with what looked like a serious knee injury before Darren Pratley doubled the advantage.
Further strikes from Cedric van der Gun and Scott Sinclair made it safe in the second period and the home side moved on to the next stage for the first time in two seasons.
Luke Moore was named in the starting line-up to make his Swansea City debut against the U's.
The former West Brom striker, who only completed his move to south west Wales two days earlier, would spearhead the Swans' attack in this third round FA Cup tie.
His inclusion was one of five changes made from the defeat against Leicester, with young defender Daniel Alfei making his senior debut for his hometown club.
The full-back, who captained the youth team to Welsh Cup success last term, played on the right side of defence with Jazz Richards continuing on the left.
Goalkeeper Yves Ma-Kalambay, Cedric van der Gun and Joe Allen were also included.
Swans:Yves Makabu-Makalambay; Daniel Alfei, Garry Monk(C) (Albert Serran, 29'), Ashley Williams, Jazz Richards; Mark Gower (Kemy Agustien, 74'), Joe Allen, Darren Pratley; Cedric van der Gun, Scott Sinclair, Luke Moore (Jermaine Easter, 83').
Subs:Dorus de Vries (GK), Casey Thomas, Stephen Dobbie, Craig Beattie.
Colchester: Ben Williams, Lee Beevers, Paul Reid, John White, Matt Heath, Andy Bond (Simon Hackney, 78'), Anthony Wordsworth, David Perkins, Kem Izzet (C) (Lloyd James, 55'), Ian Henderson (Kayode Odejayi, 55'), David Mooney.
Not Used: Mark Cousins (GK), Pat Baldwin, Steven Gillespie, Tom Bender.
Attendance: 7,005 Away: 199
Referee: R L Shoebridge (Derbyshire)
The magic of the FA Cup may not have captured the imagination of the public for this tie but the Swans certainly demonstrated their intentions to progress by the side that was selected.
Apart from the goalkeeper and two young full-backs the eight other players in white shirts have reasonable experience at playing Championship football.
One of those players was new signing Luke Moore, who only had one training sessions under his belt following the move from West Brom, and he was able to demonstrate good ball control in the early stages of his debut.
Likewise young Daniel Alfei, whose only experience of senior football has been in the reserves, looked comfortable in possession and even managed to deliver a cross into Colchester's box early on.
Colchester, though, didn't make the long trip west to sit back and soak up the pressure - home debutant 'keeper Yves Ma-Kalambay was kept busy early on and was forced into making his first save on 14 minutes, though it was an easy one as Andy Bond tried his luck from distance.
But the hosts' dominance told and by the 25th minute they were in front. Alfei and Darren Pratley linked-up to win a corner, Mark Gower's cross was cleared but from his second delivery he picked out Garry Monk at the near post to nod home and make it 1-0.
It was his first goal since finding the net against Brighton in the Carling Cup in August 2009, but within minutes joy turned to despair as he was forced off with a knee injury after coming off worse from a challenge with David Mooney.
Albert Serran was his replacement and he almost followed his skipper in getting his name on the scoresheet after being given acres of space but fired his shot straight at Ben Williams.
But within moments the Swans did double their lead - a move out of the back saw Alfei pick out Cedric van der Gun down the right, his cross had perfect weight and Pratley was perfectly placed to side foot home from 12-yards.
Half-Time: Swans 2 Colchester 0
Colchester had a spring in their step at the start of the second period and after John White fired a warning shot across goal two minutes in Ma-Kalambay used his feet to deny Mooney from close-range.
The Swans threatened in between as Jazz Richards carried the ball to byline but couldn't get his cross in while Scott Sinclair cut in from the left but lost possession.
Luke Moore was having a quiet debut but he was still making his presence known in attack and on two occasions before the hour tried to break through the U's back line only to be stopped in his tracks.
The goalscoring continued 68 minutes in to all but end this tie as a contest; quick feet by Sinclair took him past his marker and into the box, he then pulled back to the heart of the area where Cedric van der Gun was placed to pick out the bottom corner from close-range - his fourth of the season, third in cup competitions.
The Swans were enjoying complete control of this affair and with just under 10 minutes left Sinclair got in on some of the action himself - Joe Allen's through ball opened up the defence and the top-scorer took it in his stride, carried it forward and shot straight past Williams to make it four.
And it could easily have been five in the proceeding minutes, firstly when van der Gun saw his effort deflect over for a corner before Pratley found the South Stand with his volley.