The Sky Blues have beaten top of the table Luton Town 0-3 at Kenilworth Road thanks to goals from Marc McNulty, Jordan Shipley and Duckens Nazon.
McNulty gave the Sky Blues the lead after just fifteen minutes when his leapt highest to head home Jodi Jones' cross.
The game was however won in injury time. Luton's Glen Rhea was shown a straight red card for a last-man foul on McNulty and presented Shipley with a free kick just on the edge of the area, which he ferociously rocketed into the far top corner.
Finally, Nazon, who came on for Jordan Ponticelli with ten minutes to go, race down the left before cutting inside and firing home to complete a stunning solo goal and secure a hard-fought victory for the Sky Blues.
Mark Robins' side came close to taking the lead through bizarre circumstances early on. Ponticelli, making his first start for Coventry, forced Hatters 'keeper Marek Stech into a rushed clearance, which fell nicely for Liam Kelly to volley onto the crossbar from 45-yards, just inches away from an early contender for goal of the season.
Next, it was the home side's turn. James Collins, Coventry born, charged down the left before playing an inviting ball across the six-yard box but nobody was there to turn it in allowing Ryan Haynes to start the counter-attack that would give City the lead.
Jones skipped over a number of challenges before curling a splendid cross onto the head of McNulty, whose glancing header was his first goal from open play since August's 2-0 victory over Grimsby. It was against the run of play, but City were ahead.
Luton looked to respond. Collins and Danny Hylton were an obvious threat in the Hatters' attack as Luke Berry looked to thread them in on goal, but Jordan Willis and Rod McDonald did well to deal with their presence.
The home side came out after the interval just about on top. Olly Lee's precision delivery almost found a number of Luton heads as it floated across the edge of the six-yard box but nobody was quick thinking enough to turn it in.
Moments later, Ponticelli came close to finding the net on his league debut. The teenager charged to the front post to meet Jones' cross but Stech was strong enough to force his goalbound effort away.
Pelly-Ruddock Mpanzu came on just before the hour mark to replace the injured Johnny Mullins for the home side and was close to drawing Luton level with fifteen minutes to go. The midfielder fired his long-range effort inches wide of the far post.
Hylton had scored eight already this season for the home side and on another day would have ended the afternoon in double figures. With Jordan Willis on the sidelines receiving treatment, Hylton made the most of a Sky Blues side temporarily with ten men to find space in the penalty area but twice Lee Burge stood tall and denied the striker from bulging the net.
The turning point came in spectacular fashion in injury time. McNulty was sliced down while one-on-one with the 'keeper forcing referee Robert Jones no other option but to show Rhea a straight red card. Shipley, who came on only moments earlier, then arrowed a spectacular free-kick into the top corner. Two keepers would not have come close to keeping it out.
Luton were rattled, and it did not take long for Mark Robbins' side to make it three. Nazon raced away down the left before turning his defender around and firing a deflected effort over Stech with the last kick of the game. City had three goals and all three points.