The Germany midfielder was shown a straight red card by referee Mike Riley for a blatant stamp on Mohamed Sissoko.
After injury in the Community Shield hampered the start to Ballack's career at Stamford Bridge, now the German star is facing a three-match suspension for the reckless challenge which led to his 51st minute dismissal.
Drogba, however, has been inspired by the pre-season arrival of Andriy Shevchenko from AC Milan and is clearly relishing the competition from the 30 million pound Ukrainian international.
Shevchenko had a disappointing afternoon and was replaced after 65 minutes by the fit-again winger Arjen Robben.
Drogba, having already scored in three of the opening four Premiership games, conjured a lead for Chelsea out of nothing in the 42nd minute.
With his back to goal and Jamie Carragher paying close attention, the Ivory Coast international seemed to have no options as he controlled Frank Lampard's cross in a central area, 20 yards from goal,
But a smooth swivel enabled Drogba to dispatch a venomous left foot strike beyond Jose Reina.
The goal was harsh on Liverpool, who could easily have held a half-time advantage of their own.
Dutch international Dirk Kuyt rocked the crossbar with a powerful shot from the angle of the penalty area as he searched for his first goal since arriving from Feyenoord.
Later Steven Gerrard had the goal at his mercy when the ball bounced invitingly for him inside the Chelsea penalty area, but shot straight at the legs of Petr Cech.
Rafael Benitez knows that his side cannot spurn such opportunities if what he regards as the best blend of home-grown and international players he has assembled at Anfield are going to challenge Chelsea for the title this season.