Gordon Greer's late header saw Swindon progress to the third round with a 1-0 win over Wrexham who had Christian Smith sent off.
The Welsh side had the best of the chances until Smith was given a straight red for a wild lunge on Jonathan Douglas.
And he was made to pay as Swindon captain Greer nodded in from a corner with ten minutes remaining.
Wrexham made a bright start and Gareth Taylor was first to test the visitors when he met Marc Williams cut-back to force a fifth minute save from Swindon keeper David Lucas.
The pair again combined when Taylor flicked a long throw on and Williams headed just over the bar.
And the non-League side almost took a deserved lead through Ashley Westwood who met Christian Smith's 23rd minute corner at point blank range, only to see Scott Cuthbert make an instinctive block on the line.
Smith drew another fine save out of Lucas after the break before he blotted his copybook by being sent off on 52 minutes.
But Wrexham continued to fashion chances with Lucas twice pulled off brilliant saves to deny Wayne Barnes.
Yet it was Swindon who progressed when Jon-Paul McGovern's inswinging corner was met from close range by Greer.