Whittingham beat home stopper Adam Federici from fully 25 yards for his sixth goal of the season, less than 120 seconds into Saturday's match at the Madejski Stadium, to hand the Bluebirds the advantage.
And after the visitors soaked up long periods of Royals pressure as the Berkshire outfit went in search of an equaliser, Mark Hudson doubled their lead on 70 minutes to consolidate their place in the Championship play-offs - despite Jimmy Kebe's late consolation.
Cardiff, looking to extend a run of five games unbeaten, shot out of the blocks and took an early lead after just two minutes.
Reading thought they had survived an early attack, after Federici made saves from Craig Conway and Kenny Miller, but the in-form Whittingham picked up possession 25 yards from goal, spotted Federici off his line and produced a sensational dipping lob to put his side ahead.
The hosts rallied quickly and had two penalty shouts turned down by referee Darren Sheldrake in the first 10 minutes, before Noel Hunt's effort was deflected wide for a corner by Cardiff centre-back Ben Turner after he was played through on goal on 16 minutes.
Reading went close again five minutes later, as Adam Le Fondre's deft flick found Hunt in space once more but Cardiff keeper David Marshall was equal to the Irishman's effort, palming the forward's attempt to safety.
Hunt continued to be at the heart of the home side's best chances throughout the opening period, and went close with a header from Jobi McAnuff's corner.
After their early goal, Cardiff found clear-cut opportunities hard to come by, with Hudson's tame shot easily saved by Federici, but the visitors still went into the break a goal to the good.
Reading thought they had levelled 10 minutes into the second half, after Kebe ghosted in at the back post to tap home McAnuff's floated cross.
But just as the Malian was pulling away, the linesman's offside flag cut the celebrations short.
The Royals dominated the initial stages of the second period and Jem Karacan saw his effort pushed wide by Marshall, as the hosts struggled to convert territory and possession into that all-important equaliser.
With the intensity down on that of the first half, chances were few and far between for either side, but with 20 minutes remaining Cardiff grabbed their second of the afternoon.
Whittingham's free-kick found the unmarked Hudson at the near post and the centre-back guided his shot past Federici.
Reading pulled a goal back on 77 minutes, when Kebe nodded Karacan's cross past Marshall, but it was too little too late for the Royals - who slumped to their first home defeat since September 10.