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Chelsea now lead the standings with a five points ahead of Arsenal and Man. United, who are second and third respectively with the same points.
Both Chelsea and Man. United played defense game from the start, stifling each other for quite a while since the start.
Then well-organized Chelsea attacked more in the first half especially when Nicolas Anelka fired unexpectedly from the right flank on 28 minutes. But the Frenchman's effort just was melted down in easy by the 39-year-old Edwin Van der Sar, who made another fantastic one-hand stop to the French striker's curl four minutes later.
The visitors launched more offense after the break as Wayne Rooney went close from range twice. His angled shot in the 66th minute was just close to the far post and he curled the ball two minutes later to force Petr Cech a fine save.
The Blues were in front in the 76th minute when Terry jumped high to head in Frank Lampard's free-kick, but United argued furiously that Drogba was offside when the ball flew in.
Whatsoever, Chelsea could celebrate their 10th consecutive home win with a clean sheet this season and their Italian boss Carlo Ancelotti hoped the team could maintain the five-point gap.
In other matches played the day, Hull City came from behind to beat Stoke City 2-1; West Ham suffered a 1-2 home loss to Everton;Wigan and Fulham tied 1-1.