The Welshmen secured the points thanks to super calm finishes from Adrian Forbes and Lee Trundle in either half.
By contrast, Colchester have lost their first two games of the campaign, both by the same score line following a 2-1 defeat at Gillingham on Saturday.
Confident Swansea took the lead in the 35th minute when defender Alan Tate launched a long throw into the box. Powerful striker Adebayo Akinfenwa headed on and former Norwich man Forbes beat defender Sam Stockley at the far post to head past keeper Aidan Davison.
Right midfielder Forbes thought that he had scored a second goal six minutes later when he tucked home the loose ball into an unguarded net. However, referee Mr Singh had spotted a foul on keeper Davison by Akinfenwa.
Marc Goodfellow, who had a spell on loan with Colchester last season, was also close to a goal before the break, but his shot was turned around the post by a relieved Davison.
Colchester increased the tempo in the second half and Greg Halford who was close to an equaliser when he cracked a 49th minute free-kick narrowly over the bar.
Home manager Phil Parkinson made an attacking substitution in the 63rd minute replacing midfielder Kevin Watson with striker Gareth Williams and the move had an initial impact.
Only the woodwork denied Colchester in the 65th minute when Neil Danns let fly with a curling shot that struck the post from 20 yards out and rolled to safety.
The Essex club were level just a minute later. Substitute Williams fired in a shot that keeper Willy Gueret could only parry and there was Halford to sweep home the rebound.
But Colchester's joy was short lived because Swansea grabbed what proved to be the winner just a minute later.
Trundle raced onto an accurate Akinfenwa lofted pass and slotted the ball cleanly past the on-coming Davison to give the South Wales club maximum points.
The Swans must now face the tricky task of a trip to Huddersfield on Saturday as they attempt to keep their impressive 100% record intact.