Former Town employee, Luke Rooney, had put the home side a goal up before Swindon’s comeback.
Mark Cooper made just one change to the line-up; an enforced re-shuffle of the back-line saw Josh Lelan drop out and Rapha Branco step into the back three. There were also places on the bench for Second Year Scholars, Will Randall and Lee Marshall.
In a first half largely dominated by Town in terms of possession, the visitors were on the attack from the off. Nathan Byrne’s cross evaded everyone in white while seconds later, Ben Gladwin steered a shot over the crossbar.
Massimo Luongo also arrowed over while Gladwin saw his effort parried by Luton ‘keeper, Mark Tyler.
Yaser Kasim also lifted a free-kick over the bar before the home side saw efforts of their own go off target. Fraser Franks’s drive didn’t trouble Foderingham while Scott Griffiths’ effort flew wide.
Just ten minutes into the second half, the home side were awarded a spot kick. A knock-down in the box was adjudged by the linesman to have struck Nathan Thompson’s hand and the referee pointed to the spot. Former Town winger, Luke Rooney, stepped up to bury the penalty past Wes Foderingham.
Town then went back on the offensive and saw a number of half chances come and go.
With 15 minutes to play, Town levelled from the spot. Nathan Byrne burst into the box and was brought down. Michael Smith stepped up and fired the penalty low into the bottom left hand corner.
Minutes later, Town completed the turnaround. Luongo’s driving run from midfield saw him play in Smith. The Swindon number nine drifted away from the man on the edge of the box before slotting home left-footed to the delight of over 400 travelling fans.
Substitute Andy Williams forced Tyler into a good save late on as Town held on to book their place in round two.