However, both clubs attempted to defuse the situation by agreeing to scrap the traditional pre-match handshake.
After a slow start, Chelsea created the first chance of the match in the 11th minute through Mata. The Spanish winger beat two defenders but saw his powerful strike parried away to safety by QPR goalkeeper Paddy Kenny.
The R's first effort on target arrived on the hour mark courtesy of Shaun Wright-Phillips. However, Cech was able to push the former Chelsea winger's shot wide of danger.
In their very next attack, Chelsea were awarded a penalty. Mata crossed from the left and as he went to head the ball, Daniel Sturridge went down under a challenge from QPR defender Clint Hill. Referee Mike Dean pointed to the spot and Mata stepped up to send Kenny the wrong way from 12 yards.
Seven minutes of injury time were played due to an injury suffered by Chelsea midfielder Ramires and QPR almost took advantage of that time but Luke Young's low effort was tipped wide by Cech.
However, Mark Hughes's side were unable to find the goal that would have forced a replay at Stamford Bridge.