A goal from Nicky Ajose in added time helped Town to beat Wycombe Wanderers 2-1 at The County Ground.
The on-loan striker had earlier levelled for Swindon after the visitors had taken a first-half lead.
Manager Mark Cooper kept faith with the majority of the side that were knocked out of the FA Cup at Macclesfield. Tyrell Belford retained his place between the sticks while the only outfield changes were the inclusions of Nicky Ajose and Louis Thompson in place of Ryan Mason and Nile Ranger.
In a first-half with little clear-cut goalmouth action, Town had arguably the better of the chances before the visitors took the lead.
Dany N’Guessan drove wide of goal before Nicky Ajose could not quite reach Massimo Luongo’s low cross.
Alex Pritchard also fired off-target and Jay McEveley arrived on time to meet a cross from the right but could not direct his header towards goal.
With seven minutes to go before half time, Pritchard collected a neat through-ball from Luongo and took a good touch to get the ball out of his feet. With a swing of his left boot, he sent a shot goalwards which clattered off the woodwork before being cleared.
As the clock ticked into added time, Matt McClure brought down a lofted pass inside the Town box and manoeuvred his way around a pair of challenges from red shirts. He was then afforded time and space to smash the ball past Belford and give the visitors the half-time advantage.
The introduction of Ryan Harley saw him involved for Town early in the second half. His shot was deflected into the path of Ajose who saw his shot stopped on the goal-line. The pair combined again minutes later as Ajose crashed an effort into the side-netting.
Massimo Luongo saw an effort saved by Ingram before Town levelled with just under 15 minutes to play. Ryan Harley’s free-kick took a deflection on the way through with Nicky Ajose applying the final touch to help it into the net.
In added time, the man on loan from Peterborough would have the final say. A free-kick from the right dropped to the striker six yards out. Spinning on a six-pence, he tucked the ball home to send Swindon into the Area Semi-Final.
Swindon Town: Belford, Byrne, Hall, Ward (C), McEveley, Kasim, Thompson L, Luongo, Pritchard, N'Guessan, Ajose
Substitutes: Foderingham, Harley, Elgabas, Barthram, Branco