Brazilian defender Alex and the English midfielder Frank Lampard completed the scoring for the blues, which like the "reds" have the lead by 26 points but better goal difference.
Chelsea took 27 minutes to open the scoring, but once marked Alex, opened the tap for the win.
Anelka scored twice before the end of Part One. Lampard contributed to the party with the French 4-0 and the attacker closed the scoring.
"Anelka has played more than in other seasons and have more confidence," said the coach Luiz Felipe Scolari. "In every party tries to do better."
The reigning European champion, Manchester United, won by 4-3 before the revelation of the season in England, Hull City. Manchester suffered at the Hull City, back to two goals when the score to 4-1 reflected a lack of a few minutes from the end.