Robins keeper Rhys Evans made a string of fine saves but it was he who conceded the 14th minute penalty for a foul on Tony Thorpe who was making his first start for Colchester after four brief appearances as a substitute.
Up stepped leading scoring Iwelumo to send Evans the wrong way and his 17th goal of the season proved to be crucial.
There looked to be far more goals in this game which was very open from start to finish but incredibly neither side could find the net again despite numerous chances.
Before conceding the goal, Swindon had rattled the post through a fourth minute shot from Andy Nicholas.
Then late in the second half Jack Smith's downward header was brilliantly kept out by home keeper Aidan Davison.
However, it was Colchester who dictated and the Robins had their own keeper Evans to thank for at least giving them a chance.
Evans pulled off a great save to deny Thorpe a goal on his full debut, while Neil Danns and Iwelumo blew great chances to double the Essex club's lead.
However, Iwelumo's penalty at least stopped the rot as Phil Parkinson men finally secured their first win in nine matches - a dreadful run that has seen them bow out of the FA Cup and the LDV Vans Trophy as well as slipping from top spot in League One.