Ballack, playing in a deep-lying midfield role on his second debut for the club he left in 2002 for spells at Bayern Munich and Chelsea, pulled the strings as Leverkusen silenced a 73,000 crowd at Signal Iduna Park.
Dortmund will point to a disallowed goal from Sebastian Kehl shortly before Leverkusen's second as reason for complaint.
Elsewhere, on-loan striker Morten Rasmussen scored on his debut as Mainz enjoyed an impressive 2-0 win against Stuttgart.
The visitors, the best side in the Bundesliga after the winter break last season, were well beaten although they will highlight a 19th-minute penalty miss from Germany striker Cacau as a pivotal moment in the game.
Mainz took the lead shortly afterwards through Sami Allagui and Rasmussen, who joined Mainz on a season-long deal from Scottish giants Celtic last week, secured the points two minutes into the second half.