The Sky Blues came away from the County Ground with a victory thanks to goals from Amadou Bakayoko and Max Biamou.
Bakayoko latched onto a loose ball midway through the second half and made no mistake in finding the back of the net.
Then, with the last kick of the game, having only been on the pitch four minutes, Biamou fired the ball home to double City’s lead.
It was the hosts who had the first opportunity of the game as a long ball played forward was brought down well by Mathieu Baudry and he looked to test Marko Marosi, but the shot was tame and comfortable for the ‘keeper.
The Sky Blues had to wait just two minutes for their first effort, and it was Liam Kelly’s ball forward which was well taken by Wesley Jobello and he found the run of Jamie Allen, however his shot went wide.
City started to take control of the game from then on and went close to an opener when Jordan Shipley’s free-kick was met by Kyle McFadzean, but he couldn’t direct his header towards goal.
However, it was Swindon who came the closest to opening the scoring, but they were denied by a superb Marosi save to deny Michael Doughty from six yards out.
A few minutes later and it was Luke McCormick in the other goal who was called into action, as he got down to his near post to deny a driven shot by Liam Kelly.
That would prove the last piece of action in the first half and after the break it was City who almost took the lead. A bursting run forward by Tom Bayliss, who replaced Kelly, and he picked out Jobello, who beat his man and found Bakayoko, but his shot was saved.
Moments later, Jerry Yates missed a guilt-edge opportunity for the host after he was played through one on one with Marosi, he sent his shot well wide.
Swindon would be left to rue that missed chance as on 57 minutes Bakayoko intercepted a loose ball at the back and punished Mathieu Baudry’s error by rounding the ‘keeper and slotting the ball into an empty net to give City the lead.
City continued to apply pressure and some good work from Hiwula created an opening for a shot from distance, however, his shot flew over the bar.
Richie Wellens side almost found an equaliser ten minutes from time, but they were denied by a superb goal-line clearance by Kyle McFadzean to deny Yates.
After coming on in the 86th minute, Max Biamou took only four minutes to find the back of the net, smashing the ball past Luke McCormick with the last kick of the game.
Goals: Bakayoko 57’, Biamou 90’
Referee: Andy Woolmer
Sky Blues Xl: Marko Marosi (GK), Fankaty Dabo, Michael Rose (61’ Pask), Kyle McFadzean, Brandon Mason, Liam Kelly (C) (44’ Bayliss), Jamie Allen (46’ Westbrooke), Jordan Shipley, Wesley Jobello (86’ Bapaga), Jordy Hiwula, Amadou Bakayoko (86’ Biamou).
Unused Subs: Ben Wilson (GK), Sam McCallum, Declan Drysdale.
Swindon Town Xl: Luke McCormick (GK), Zeke Fryers, Mathieu Baudry, Trialist, Adam May, Jerry Yates, Michael Doughty, Kaiyne Woolery, Jordan Lyden, Rob Hunt, Dion Conroy.
Subs: Tyler Reid, Tom Broadbent, Trialist, Dan Ballard, Scott Twine, Trialist, Taylor Curran, Ralph Graham, Joe Romanski.