Duckens Nazon's second-half screamer sends the Sky Blues away from the County Ground with all three points.
Luke Norris did give the home side the lead early on with a spectacular volley but Michael Doyle pounced mid-way through the first half the draw City level.
James Dunne was shown a straight red card after an altercation with Doyle as the game drew to a close, giving Coventry enough time to punish the Robins with ten minutes to go.
All of the game's early chance under the floodlights in Wiltshere fell to Max Biamou, in for the injured Peter Vincenti. For the first, City's number nine forced a strong save out of Lawrence Vigouroux from a tight angle after just two minutes, something he would do a number of times throughout the first half.
Ninety seconds later and Biamou found himself in again, but this time the former Sutton man came together with Chris Robertson on the edge of the area, leaving both in heap. Those in Sky Blue felt insensed that the referee chose to take no action but after a look over at his official the officials waved play on.
It was clear for all to see that the Sky Blues had started the stonger, but Swindon were prensented with a golden chance to take the lead ten minutes in. Matty Taylor's left foot has built him quite a reputation over the years but on this occasion his clever free-kick went under the wall and wide of the near post.
The Robins grew in confidence as the half went on and it would be the home side who opened the scoring on the twentieth minute. Keshi Anderson's stunning charge forward help to set up a ball to Luke Norris, who on the turn sent a thunderous volley past Lee Burge into the top corner.
Ten minutes later though and City had their responce. Jodi Jones broke away down the left before playing his cross low and hard across the area that, after a deflection, rolled perfectly into the path of Doyle who slammed the ball home from close range. The captain had City level.
The second period started with another slice of controversy. Nazon used his pace to charge down Robertson, knicking the ball off his toe in the area before the number five seemed to bring him down. Again though the officials ruled no foul.
Doyle had been ruffling Robin's feathers all evening, and after an altercation with Dunne the Swindon man was shown a straight red card for raising his hands with Coventry's captain going into the book for his involvment.
The Sky Blues made the extra man count. Five minutes later, Nazon submitted his entry for Goal of the Season as he side-stepped inside a curled a beauty into the far top corner from 30-yards. Vigouroux has been outstanding for Swindon this season, but even he could only watch as Nazon's effort flew in under the cross bar.
Seven minutes added time gave the game some late tension, but amongst all the pressure of Swindon trying to draw level it was Nazon again who was presented with the best chance. His delicate flick over the keeper bounced agonisingly just wide of the far post, but it did not matter. City had taken all three points.
Red: Dunne 71'
Yellow: Doyle 71', McDonald 73', Nazon 76'.
Coventry City XI: Burge (GK), Grimmer, Willis, McDonald, Stokes (Davies 89'), Kelly, Doyle (C), Jones (Shipley 80'), Dev. Kelly-Evans, Nazon, Biamou (McNulty 90').
Coventry City Subs: O'Brien (GK), Di. Kelly-Evans, Maycock, Ponticelli.
Swindon Town XI: Vigourouz (GK), Purkiss, Lancashire (C), Robertson, Taylor, Dunne, Elsnik (Linganzi 65'), Mullin (McDermott 58'), Anderson, Gordon (Smith 81'), Norris.
Swindon Town Subs: Charles-Cook (GK), Preston, Knoyle, Woolery.