The crucial Championship clash looked to be heading for a draw before referee Simon Hooper awarded a stoppage-time penalty on the basis of his assistant's opinion that defender Martin Cranie had handled.
Whittingham, who had earlier missed from two yards, fired in the spot-kick to win it for Dave Jones' team.
It had been a scrappy start to the first half with Cardiff dominating possession but making very little use of it. Coventry striker Clinton Morrison carved himself a half-chance in the 16th minute but he shot into the side-netting from a very tight angle.
Chris Coleman's team started to come into it and Morrison went close with a header from Cranie's cross in the 18th minute but his effort drifted just wide.
Then, two minutes later, Michael McIndoe and Jonathan Stead combined to set up Irish midfielder Gary Deegan but he shot wide when he could have played in Morrison.
Whittingham had a sight of goal in the 25th minute but he fired high over the bar from distance.
The home side took the lead and it was Morrison who found the net for City in the 32nd minute. Aron Gunnarsson sent in a long throw from the right, James McPake helped it on to the back post and Morrison headed in from a yard out for his 11th of the season.
The visitors had a chance to hit straight back when Chris Burke crossed from the right wing but Darcy Blake headed over the crossbar.
Whittingham had the ball in the net in the 40th minute but it was ruled out for offside. Just seconds later, however, Cardiff were back on level terms. Coventry failed to deal with a flick from Jay Bothroyd and, as the home defence hesitated, Burke stole in and shot home from ten yards.
Cardiff had two great chances to go ahead after half-time. Whittingham missed from right under the crossbar after Mark Kennedy's fiercely struck cross.
Then Ross McCormack went through on goal but shot straight at Coventry keeper Keiren Westwood.
The Cardiff striker nearly made amends in the 62nd minute but his smashed free-kick was palmed away by Westwood and headed clear by Richard Wood.
Carl Baker finished off a 78th-minute run with a shot inside the box which was blocked by a Cardiff body and left Coventry claiming a penalty for handball.
Coventry's claims were waved away but, 12 minutes later, Cardiff were given a penalty and Whittingham's cool spot-kick won it.