After an even start which saw both sides mount attacks - including a miss from Arsenal's Olivier Giroud - the hosting Blues broke the deadlock in controversial circumstances with six minutes played. Ramires appeared to foul Arsenal midfielder Francis Coquelin on the halfway line, but referee Martin Atkinson allowed play to continue.
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Having gone in front, Chelsea began to dominate the contest and they went on to double their advantage ten minutes later.
Brazilian international Ramires went to take the ball beyond Szczesny, but the Arsenal keeper halted his run by bringing him down inside the area. The Polish international escaped with only a yellow card, but he was unable to prevent Lampard from sending the resultant penalty into bottom-right hand corner of the net.
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Chelsea continued to be the dominant force and almost added a third with 35 minutes played when a counter-attack move ended with Eden Hazard crossing for Ramires, but the midfielder sent his effort just over the crossbar.
Should the home team hold out for all three points, they will close the gap on leaders Manchester United to 10 points.