Mark Cooper’s side were forced to play with ten men for over 70 minutes after captain Nathan Thompson had been sent off in the 21st minute for a professional foul but further defensive lapses made Cheltenham’s job easier with Byron Harrison scoring a hat trick.
The Swindon manager made two changes to his line up with Nathan Byrne and Andy Williams starting in place of Ben Gladwin and Michael Smith.
Town kicked off in their new day-glow Purple kit playing towards the 1566 visiting supporters and went straight on the attack until Byrne lost possession in the penalty area.
Former Town player Raffaele De Vita conceded a free kick just outside the penalty area but Town were penalised for pushing when the ball was crossed and the chance was gone.
Town were rocked when Byron Harrison gave Cheltenham the lead in the 10th minute after nipping in front of Foderingham as the ball ran towards the Town penalty area and after sidestepping the Town keeper, Harrison had the simple task of tapping the ball into the empty net.
The goal silenced the Town fans after a good start for the Robins but eventually Louis Thompson tried his luck from 30 yards with a powerful shot which was well caught by Trevor Carson in the home goal.
Town’s first corner in the 19th minute was wasted with the ball striking the nearest defender but they did have a goalscoring attempt shortly afterwards when Obika headed straight at Carson who saved easily.
Disaster struck for Swindon in the 20th minute when Nathan Thompson was shown the red card for hauling back Terry Gornell approximately 30 yards from goal with the referee taking some time to make his mind up.
The enforced change saw Louis Thompson taking over his brother’s position of right back with Town now playing 342 but they continued to play their short passing game to try and bypass the home defence.
Cheltenham earned a corner in the 35th minute when a cross was deflected behind and Foderingham did well to push the resulting header around the post. However the home side continued to press and De Vita’s cross to the back post in the 36th minute saw Terry Gornell double the lead for the Gloucestershire team.
Craig Braham-Barrett was cautioned in the 38th minute for simulation after tumbling under a challenge by Byrne.
De Vita was clearly enjoying playing against his former employers and he went close to opening his goalscoring account with a fine run into the penalty area before firing a powerful shot against the post and the ball went out for a goal kick.
Andy Williams tried his luck at the other end with a shot from 20 plus yards but his effort was always rising and did not trouble the keeper.
Two minutes of added time were played with no major incidents to report at either end of the field so it was the Gloucestershire Robins who left the field flying high at half time.
Town had a corner in the 48th minute which was cleared but they were awarded a free kick when Toffolo had his shirt pulled but Kasim’s low shot struck the defensive wall. Kasim had another chance shortly afterwards from a free kick near the corner flag but his curling effort evaded everyone and the ball flew out for a goal kick.
Cheltenham’s first attack of the half resulted in a goal when Jack Stephens tried to shepherd the ball out of play but Braham-Barrett chased hard and crossed for Byron Harrison to tap home from close range in the 53rd minute.
Mark Cooper responded by replacing Obika with Michael Smith in the 56th minute with the game slipping away from 10 man Swindon.
Raffa De Vita almost embarrassed Town further in the 59th minute when he ghosted in behlnd the Town defence to volley just over the bar with Foderingham beaten.
Raphael Rossi-Branco made a welcome return from injury in the 62nd minute replacing Jack Stephens.
Yaser Kasim earned a corner for Town after some determined running but his cross from the corner struck a defender and the ball was cleared.
Nathan Byrne came closest to pulling a goal back in the 64th minute with a powerful shot from 30 yards but the ball struck the inside of the post and rebounded to safety.
Cheltenham had a corner in the 67th minute when Turnbull headed a cross behind but Foderingham caught the cross under pressure.
Jordan Turnbull was cautioned in the 72nd h minute for fouling De Vita near the dugouts and eventually earned a corner which saw Elliott’s shot strike the post. However the ball pinged around the penalty area and when it was eventually cleared it fell nicely for Matt Richards who thundered in a 25 yard shot to give Cheltenham a four goal lead.
John Marquis replaced Gornell for the home side in the 77th minute and he was presented with a gift wrapped chance within a minute when Rossi-Branco’s slip gifted him possession but Marquis fired wide of goal under pressure from the advancing Foderingham.
Michael Smith’s mishit shot in the 80th minute earned a corner and while there was a break in play, Ben Gladwin replaced Kasim.
Cheltenham went nap in the 84th minute after a weak chested backpass by Branco sold Foderingham short and Byron Harrison nipped in to tap home for a hat trick as good reward for his Man of the Match performance for the home side.
Zack Kotwica replaced Braham-Barrett early in the 4 minutes of added time for the home side.
The ten men of Swindon managed to keep the rampant Cheltenham forwards at bay in added time so the match ended with Cheltenham’s name in Monday’s draw for Round Two while Swindon must now regroup and focus on next week’s League One match at home to Bristol City.