Whittingham, a former Aston Villa trainee born in Nuneaton, blasted home from the spot after Martin Cranie was controversially adjudged to have handled his attempted cross by the referee's assistant.
Whittingham's winner only served to make up for his gilt-edged second-half miss that will surely go down as one of the worst of the season.
And David Bell still almost snatched a point for Coventry when he headed against the bar in the last minute.
The in-form Sky Blues, having lost one of their last 10, went into Tuesday night's Championship clash at the Ricoh Arena knowing victory could see them leapfrog their opponents into the final play-off berth.
And they took the lead just after the half-hour mark when Clinton Morrison was on hand to head in his 11th league goal of the season at the far post following Aron Gunnarsson's long throw.
But the cash-strapped Bluebirds, currently struggling both on and off the pitch, levelled just before the break through Chris Burke's opportunist finish from six yards.
Cardiff's away support waved several Malaysian flags prior to kick-off in support of potential investment from the Far East.
And despite their current travel sickness, the visiting contingent of 674 watched their side settle the better of the two during the opening 15 minutes, playing plenty of passing football that was easy on the eye.
Yet it was Morrison who headed the first chance wide after 19 minutes as the Sky Blues took the upper hand.
The prospect of an exciting, end-to-end promotion tussle was appearing to vanish as the half wore on, with almost all of the action taking place in the middle of the park.
Bluebirds goalkeeper David Marshall saved well from Carl Baker's set-piece, although the whistle had blown for offside.
But the roof was well and truly raised in the 32nd minute as the Sky Blues capitalised on Gunnarsson's throw-in.
The Iceland international launched the ball goalwards, James McPake flicked it on and Morrison was on hand unmarked to stoop at the far post.
Whittingham slotted home in the 39th minute although he was judged to be offside, with the decision a tight one.
Nevertheless, the visitors were level two minutes later when the home defence failed to deal with Jay Bothroyd's clipped cross into the area and the bouncing ball broke for Burke to fire past Keiren Westwood, who was beaten before he even had the chance to make a save.
The sides went in level at the break but Cardiff could and should have been out of sight within 10 minutes of the restart.
Firstly Whittingham somehow blazed over the bar from two yards with the goal at his mercy.
And just minutes later, Ross McCormack failed to connect properly with his shot having been sent clear.
The Scot then tested the fingers of Westwood with a fierce free-kick as the game opened up and chances started to come.
Bothroyd and Anthony Gerrard both went close before the home faithful were enraged by the penalty decision, which Whittingham duly gobbled up.
There was still time for substitute Bell to head against the woodwork but it was the visitors who went home happy at the final whistle.