The Ivorian striker's 43rd minute winner gave Chelsea their 12th point of the season and halted Liverpool's tally at 4 points.
Chelsea played the majority of the second-half with 10 men after German midfielder was sent-off for a rash tackle on Malian midfielder Momo Sissoko.
Liverpool dominated the majority of the first-half and had first crack on goal as early as the 16th minute when Dirk Kuyt unleashed a fierce drive that smashed off the crossbar.
Reds keeper Pepe Reina was brought into action with a powerful free-kick from Frank Lampard.
With two minutes to play in the first-half, Lampard picked out Drogba with a perfect cross from the right.
The Ivorian ace controlled the ball on his chest and turned guide home a dazzling left-footed volley that left Reina motionless.
The game became more physical and ill-tempered after the interval as Ballack stamped on the physical Sissoko six minutes after re-start.
Chelsea had keeper Petr Cech to thank for maintaining the score-line with a brilliant save to Steven Gerrard's shot from point-blank range.
Gerrard also had a penalty claim waved off by the referee as Chelsea held on to grab the victory.