Drogba, on the edge of the area, collected a Frank Lampard pass with his back to goal and swivelled round to smash a blistering half-volley past Liverpool keeper Jose Reina four minutes before halftime.
The match at Stamford Bridge began to swing Liverpool's way soon after the re-start when Ballack brought his boot down on the thigh of Liverpool's Mali international midfielder Momo Sissoko.
But despite the red card for Germany's World Cup captain, playing only his fifth game since a close season move from Bayern Munich, Chelsea stuck their task.
Penalty appeals were waved away at both ends, while Liverpool skipper Steven Gerrard missed a golden opportunity to equalise, drilling the ball straight at keeper Petr Cech from close range.
The victory over a potential title rival hoisted Chelsea into third place on 12 points.
Manchester United were just ahead of the champions on goal difference before their late kickoff against Arsenal in Sunday's other showcase game. Portsmouth were top on 13.
Premier League action was continuing on Sunday with three other games.
