The visitors took the lead in the 66th minute through Romain Vincelot from close range and they went further ahead in the 81st minute when Marcus Tudgay fired home after his penalty had initially been saved by Lawrence Vigouroux.
However Ben Gladwin’s first goal back in Town colours gave hope to the Robins and the recovery was completed in added time when Nicky Ajose slotted home from the penalty spot after a defender had handled in the penalty area.
Swindon lined up with Jordan Turnbull back after suspension and there was a starting places for Henrik Ojamaa with Brandon Ormonde-Ottewill and Drissa Traore dropping down to the bench. The Sky Blues line up included Jacob Murphy and Sam Ricketts who had both previously played for the Robins and Joe Cole started on loan from Aston Villa.
Town kicked off the match playing towards the Stratton Bank but is the Coventry’s Adam Armstrong who had the first shot of the match when he fired wide from 20 yards but his effort went wide of the upright.
The visitors earned a corner shortly afterwards when Turnbull blocked a cross from the right wing but the Town defence cleared downfield.
Town were starting to get some passing moves going in midfield with Rodgers looking to set up Ajose on the edge of the area but the ball stuck under his feet and the chance was gone.
Jordan Turnbull tried his luck from 20 yards but the keeper smothered the ball at the second attempt.
Jim O’Brien also fired in a long range shot which went over the crossbar in the 22nd minute.
Ben Gladwin seized possession in midfield before jinking past several defenders then firing in a powerful shot which was well caught by Reice Charles-Cook in goal. Gladwin then had another great chance when he beat Jim O’Brien, who injured himself, but the Town midfielder then lost possession on the edge of the area. O’Brien was able to continue after some treatment by the physio.
Gladwin tried his luck from 30 yards with a long range freekick in the 34th minute which the goalkeeper initially parried but just regained possession with Ajose nearby.
Yaser Kasim was cautioned in the 38th minute for shirt pulling near the halfway line.
Town were continuing to get plenty of possession as the half wore on without finding the elusive shot on goal.
Ben Gladwin fired in a shot as the match neared added time but the keeper caught the ball before launching an attack which led to Bradley Barry kicking the ball of the line from a shot by Cole to deny Coventry a half time lead.
The visitors replaced Joe Cole at half time with Ruben Lameiras.
Adam El Abd’s determination saw him advance downfield before laying off the ball to Brophy and he passed the ball to Ojamaa but his effort struck a defender and the chance was gone.
Nicky Ajose went close moments later after a good move had seen Ojamaa send in a hard cross from the right wing where Ajose tried a backheeled effort which the keeper took cleanly.
El Abd made an outstanding tackle to deny Ryan Kent who was charging towards goal in the 53rd minute.
Romain Vincelot saw yellow for a late tackle on Kasim in the 53rd minute.
Town were continuing to press forward probing for an opening with Brophy seeing plenty of the ball down the left wing.
Kent was replaced by Jacob Murphy in the 60th minute for the Sky Blues.
Town carved out a chance in the 62nd minute through Ojamaa who laid the ball off to Gladwin on the edge of the area but his shot was always rising and went over the bar.
Jon Obika replaced James Brophy who received a superb ovation after a strong display for the Robins and Fabien Robert replaced Ojamaa in the 64th minute.
Coventry took the lead in the 66th minute when Stokes crossed from the left wing and Vigouroux could only get his fingertips to the ball leaving Vincelot to slot home from close range to delight the 1686 Sky Blues
supporters in the crowd of 8309.
Adam Armstrong also had a chance shortly afterwards but he dragged his shot across goal.
Barry was shown a yellow card in the 74th minute for a late challenge on Murphy near the centre circle just as he was about to charge downfield.
Town were pressing hard for an equaliser but the visiting defence were dealing with everything that the Robins could throw at them.
Marcus Tudgay replaced Armstrong in the 78th minute as Town waited to take a corner and that led to a goalmouth scramble ending in another corner but the keeper caught the resulting cross cleanly.
The Sky Blues were awarded a penalty in the 80th minute when El Abd was adjudged to have held an attacker back and although Vigouroux parried Tudgay’s shot, the Coventry attacker reacted quickest and made no mistake with his second chance.
John Fleck was shown yellow for pulling Robert’s shirt in the 84th minute.
Ben Gladwin pulled a goal back for the Robins in the 85th minute when he received the ball on the edge of the area and he took a couple of paces forward before blasting past the keeper to give renewed hope to the Town fans.
Town were awarded a lifeline in the seconnd minute of added time when a defender handled the ball and up stepped Nicky Ajose to calmly slot the ball to the left of the keeper who went the wrong way.
The noise cranked up around the County Ground when Town were awarded a corner which led to some heavy pressure and the final whistle was greeted with a tremendous roar by the home fans after seeing a superb comeback by the Robins.