QPR 0-1 Chelsea
Juan Mata's controversial second-half penalty earned Chelsea victory over west London rivals QPR and sent them into the fifth round of the FA Cup.
Mata scored from 12 yards after Clint Hill was adjudged to have barged over Daniel Sturridge, a decision that looked harsh on replays.
Moments earlier, Chelsea had claimed a penalty when Hill tripped Sturridge.
In a game of few chances, Mata forced a low save from Paddy Kenny, while Ramires .
Much of the pre-match talk centred on whether there would be a conciliatory handshake between John Terry and Anton Ferdinand, in the first meeting between the sides since in October's Premier League game.
But neither player was given the option as the Football Association announced before kick-off that there would be no customary pre-match handshakes between the sides.
While the atmosphere was fiery off the pitch, on it both sides played out a poor first half which lacked creativity.
Mata had the only clear chance, forcing Kenny into a decent low save from the edge of the box after seizing on Luke Young's slip.
Joey Barton wasted QPR's best effort, a half-volley from 20 yards which went comfortably wide of Petr Cech's post.
Mata was the game's outstanding player and his delightful back heel played in Ramires, but the Brazilian's delivery across the face of the goal was missed by the Chelsea forward line.
Chelsea started the second half brightly and Sturridge went close, sending a fierce drive from the edge of the area narrowly wide after Fernando Torres played him in.
QPR were struggling to get a foothold in the game and had no penetration up front, despite the introduction of Federico Macheda at half-time.
The visitors were aggrieved not to win a penalty after Hill's challenge on the lively Sturridge, but referee Mike Dean waved away appeals.
However, moments later Chelsea were awarded a penalty that looked less obvious when Hill was deemed to have bundled over Sturridge, who went to ground easily.
Mata dispatched the penalty expertly, sending Kenny the wrong way and finding the bottom left-hand corner of the net to give Chelsea a 60th-minute lead.
The action on the pitch led to some unsavoury incidents off it, with reports of objects being thrown by fans, while Dean spoke with a steward in the crowd about another incident during a break in play.
With 15 minutes remaining, Ramires blocked a shot from Hill, leading to a lengthy delay and the Chelsea player being carried off on a stretcher with suspected knee ligament damage.
The delay hindered QPR's attempts for an equaliser, with Mark Hughes's side finding it near impossible to gain any momentum and penetrate Chelsea's defence.
But the announcement of seven minutes of injury time spurred them on and, in the final seconds, Young forced a decent low save from Cech before Shaun Wright-Phillips's volley missed the target.