The Spain midfielder rifled a low left-footer past Paddy Kenny on 61 minutes after Clint Hill bundled over Daniel Sturridge.
The match was terrible as a football game but enthralling for all the off-field build-up.
The return of Chelsea to a stadium where they lost In controversial circumstances in October, where John Terry was cited for racial abusive behaviour and where two Blues players were sent off.
By contrast this game was anaemic and desperate in need of a football transfusion. But it was not to be.
The FA scrapped the normal pre-match handshake for the game in order to defuse any potential tensions.
As for the game, neither made much of an attempt in the opening exchanges to attack,Mather leaving it to the defence to play among themselves.
Frustration finally got the better of Chelsea, when on nine minutes, Daniel Sturridge tested not Paddy Kenny in the QPR goal, but row Z instead from long range.
Two inputs later and following a quick counter attack, Juan Mata took advantage of a slip by Clint Hill and raced Clark. Kenny, in goal was qual to the fine strike from 20 yards and parried the ball to safety.
Joey Barton had the home side's first effort, half-hearted half volley from distance which was well wide of Petr Cech's goal.
Ex-Chelsea winger Shaun Wright-Philips tried. Mazy run on Branislav Ivanovic on 36 minutes, but he too skied his final effort on goal.
Chelsea by contrast carved out several good opportunities, but each time the final ball was either wayward in its delivery or Fernando Torres was not in place receive it. No changes are made to personal at half-time to excite the 15,728 crowd of which 3, 114 were Chelsea fans.
It was the visitors who had the first chance of the half on 52 minutes, with Torres the architect, setting up Sturridge to flash a blistering left footer from just outside the area, which whizzed just over the QPR crossbar.
David Luiz followed that up with a speculative 30-yarder which was simply embarrassing in its ineptitude.
On 60 minutes, Wright-Philips skinned Cole on the left but his byline cross could not be put away.
Seconds later and the Blues were awarded a penalty when Clint Hill was judged by referee Mike Dean to have upended Daniel Sturridge in the six-yard box.
It looked soft but Mata stepped up in the absence of injured Frank Lampard and tucked the ball home confidently past Kenny.
Oriol Romeu replaced Ramires on 77 minutes after the Brazil midfielder fell awkwardly. He needed treatment for around five minutes before being stretchered off. QPR took the opportunity to replace Jamie Mackie for Robert Hulse.
Cech was forced into making a fine diving save to his right deep into the seven added minutes by was never seriously tested by the home side.
Mark Hughes can now concentrate on their relaxation plight while Andres Villas-Boas can look forward to a tilt attune last remaining silverware at his disposal.
If they play to many games like this again, they won't be booking a date at Wembley in May. Teams. QPR -Kenny, Hill, Hall. JACKIE, Buzsaky, Barton, Young, Smith, Helguson, Wright-Philips, Ferdinand. subs, Cerny, Orr, Derry, Hulse, Ephraim, Macheda, Onuoha. Chelsea, - Cech, Ivanovic, Cole, Luiz, Ramires, Torres, Mata, Maliuda, Meireles, Sturridge, Terry. Subs, Turnbull, Essien, Romeu, Bosingwa, Lukaku Cahill Bertrand.