Coventry striker Ellis Simms scored his 11th goal in seven games when he turned in Milan van Ewijk’s low cross to put the hosts in front.
Kitching lashed the ball into the roof of his own net under pressure from Cardiff’s Josh Bowler at a corner to bring the visitors level before half-time.
Then after the break, a Bowler cross deflected off the unfortunate Kitching and looped into the net.
Haji Wright thought he had equalised for Coventry with six minutes left, but his header was ruled out for offside.
The end of Coventry’s three-match winning run means the Sky Blues stay seventh in the Championship table, having missed the opportunity to close the four-point gap between themselves and sixth-placed Norwich, who lost at Leicester earlier in the day.
Cardiff remain 11th after an excellent response to losing back-to-back league games.
Few would have given Erol Bulut’s men a hope of winning at Coventry beforehand, but they fought back superbly after falling behind against Mark Robins’ play-off chasers.
Simms has been central to Coventry’s recent fine form – scoring more goals in all competitions in 2024 than anyone else in the top four English divisions – and he saw an early goal-bound effort blocked by Jamilu Collins.
After Ben Sheaf hit a 20-yard shot narrowly over, the hosts then had they deserved when a slick team move ended with Simms tapping in from Van Ewijk’s right-wing cross.
Set-piece kings Cardiff still posed a threat, though. Nat Phillips fired a warning when his header was saved but, from another corner soon afterwards, his nod-down was not cleared properly and, under pressure from Bowler, Kitching smashed the ball into the roof of his own net.
Bowler was close to scoring a sensational goal less than a minute into the second half when his powerful left-footed shot from over 30 yards swerved just wide of the far post.
