Ballack headed in Paulo Ferreira's right-wing cross in the 32nd minute as the Blues dominated the first half.
They were unable to score again in a nervy second half while Reading failed to make the most of several set-pieces.
The result meant Chelsea equalled a club record of nine successive wins in all competitions set in 2005.
It also meant that Avram Grant's record in his first 29 wins is exactly the same as Jose Mourinho's.
Reading midfielder Stephen Hunt was booed throughout by the home fans after his collision with Petr Cech last season saw the Chelsea goalkeeper suffer a fractured skull - and was later on the receiving end of a fierce two-footed challenge from Alex that went unpunished.