Adebayo Akinfenwa's first-leg goal gave Swansea a slender lead to take to Colchester next week in the LDV Vans Trophy southern section final.
Adebayo Akinfenwa's goal gave Swansea a slender lead
The striker struck on 40 minutes when he controlled Kevin McLeod's flick-on and turned inside two men to score.
Colchester should have been in the lead by then, but Chris Iwelumo failed with Swans goalkeeper Willy Gueret to beat.
Swansea could have made it two in the second half, but Dean Gerken saved well from Lee Trundle to keep the tie alive.
Swansea: Gueret, Ricketts (MacDonald 74), Tate, Monk, Forbes, Britton, McLeod (Martinez 67), Robinson, Way, Akinfenwa, Trundle (Knight 68). Subs Not Used: Murphy, Bond.
Goals: Akinfenwa 40.
Colchester: Gerken, Brown, Elokobi (Izzet 89), Chilvers, Stockley, Danns, Watson, Duguid, Garcia (Baldwin 60), Williams (Guy 83), Iwelumo. Subs Not Used: Richards, Cousins.
Ref: P Taylor (Hertfordshire).