Nigel Starkey's side, who had done very well to reach this stage of the competition, went behind in the 13th minute through Josh Parsons and nine minutes late, Seb Broomfield headed a second for Paul Boden's side.
Straight from the restart, Swindon won back possession and Josh Parsons scored a second with a low drive.
Sphinx rallied and it was not until the 48th minute that Swindon added a fourth through Miles Storey.
In the 77th minute, there was some consolation for the travelling Sphinx support when Adam Bilic steered home from a Brad Taylor header.
Five minutes from time, Ben Whitehead scored a fifth for Swindon and in third minute of stoppage time, Storey hit the his second of the game to give Swindon a 6-1 victory.
Swindon report
http://www.swindontownfc.co.uk/page/NewsDetail/0,,10341~2222529,00.html