Sky Blues fan James Collins scored against the team he has supported since childhood as his side fought back.
Paolo di Canio's side looked to be heading for a surprise defeat after David McGoldrick's first-half double had put the struggling Sky Blues in control.
Gary Roberts' 77th-minute strike followed by substitute Collins' powerfully-struck volley three minutes later earned the promotion-chasers an unlikely point.
Swindon winger Matt Ritchie saw his second-minute shot strike the post before McGoldrick headed in John Fleck's left-wing free-kick after 13 minutes.
Striker McGoldrick doubled his and the visitors' tally eight minutes before half-time, rifling home from 10 yards after Swindon goalkeeper Wes Foderingham flapped at a Fleck corner.
Roberts reduced the arrears by volleying in from six yards after Tommy Miller had flicked on Alan Navarro's corner and Collins completed the comeback soon after with a stunning shot from the edge of the penalty area after Jay McEveley had centred.