Substitute Joe Cole strengthened Chelsea's grip on the Premiership lead with a late winner at Anfield.
Cole earned Chelsea a vital victory when his shot was deflected past Liverpool goalkeeper Jerzy Dudek by Jamie Carragher after 80 minutes.
Liverpool were left cursing referee Mike Riley, who turned down first-half penalty appeals when Tiago handled.
Chelsea goalkeeper Petr Cech saved well from Djimi Traore, while Liverpool lost Xabi Alonso with a broken ankle.
Liverpool were still without leading goalscorer Milan Baros, who was ruled out with a hamstring injury.
The opening chance of a first-half dominated by Liverpool fell to the unlikely figure of Traore, who could only shoot straight at Cech after being set up by Florent Sinama Pongolle.
Chelsea stuttered their way through the opening period, but created the best chance when Robben raced clear, but Dudek guessed right and saved low down.
Liverpool lost influential midfield man Alonso after 27 minutes, when he limped off with what was later diagnosed as a broken ankle following a tackle from Frank Lampard that earned the England midfield man a booking.
Chelsea's defence had stood firm in front of Cech, but he needed to produce a fine reaction save to deny Antonio Nunez after Tiago struck a clearance straight at the Liverpool substitute.
Anfield erupted in anger just before the break when Tiago clearly handled under pressure from Nunez.
Referee Riley appeared to raise his whistle to his lips before waving play on.
Chelsea had the first chance of the second half, Damien Duff's inviting cross just eluding Eidur Gudjohnsen as he stretched in front of an open goal.
It was Gudjohnsen's final contribution, as he was taken off on the hour and replaced by Didier Drogba.
Chelsea made another familiar change with 15 minutes left, sending on Cole for Duff.
And Cole broke the deadlock five minutes later, when his shot from edge of the area clipped off Carragher and deceived Dudek.
Liverpool: Dudek, Finnan, Hyypia, Carragher, Traore,
Luis Garcia, Gerrard, Hamann, Alonso (Nunez 27),
Riise (Mellor 86), Sinama Pongolle.
Subs Not Used: Diao, Warnock, Harrison.
Booked: Luis Garcia, Hamann.
Chelsea: Cech, Paulo Ferreira, Terry, Gallas, Johnson, Tiago,
Lampard, Makelele, Duff (Cole 76), Robben (Kezman 83),
Gudjohnsen (Drogba 61).
Subs Not Used: Cudicini, Geremi.
Booked: Lampard, Johnson.
Goals: Cole 80.
Ref: M Riley (W Yorkshire).