Ballack enjoys winning return with Leverkusen
Champions Bayern Munich edged past VfB Wolfsburg 2-1 with a stoppage-time goal through Bastian Schweinsteiger on Friday, while Hamburg SV beat last season's runners-up Schalke 04 2-1 on Saturday.
Ballack, who played for Leverkusen until his 2002 move to Bayern Munich, returned from Chelsea in the close season.
"What I am still lacking is power," said the 33-year-old midfielder, who lasted the full 90 minutes after recovering from an ankle injury that saw him miss the World Cup in South Africa.
"But I am happy I played the full game. The coach asked me a few times but I was just happy to play through."
Leverkusen, among the title favourites, grabbed a deserved lead in the 19th minute when Tranquillo Barnetta completed a swift passing move between him, Gonzalo Castro and Arturo Vidal that left the defence dazed.
With Dortmund still rattled by the goal, Leverkusen struck again three minutes later with a solo effort from Renato Augusto.
Dortmund tried to cut the deficit in the second half and Nuri Sahin came close but his curled free-kick was palmed over the bar by Germany international keeper Rene Adler.
Mainz kicked off their Bundesliga season with an impressive 2-0 victory over visitors VfB Stuttgart, with both goals coming from new signings.
Mainz struck midway through the first half, though it was Stuttgart who had the biggest chance to take the lead when Cacau's penalty was saved in the 18th minute.
Tunisia striker Sami Allagui slotted home from the edge of the box in the 26th minute before Morten Rasmussen, on loan from Celtic, doubled their lead with a dipping header from 16 metres early in the second half.
The hosts missed several chances and Adam Szalai even rattled the crossbar in the 74th minute with a fierce drive as Stuttgart's defence was in complete disarray.
Stuttgart take on Slovan Bratislava on Thursday in the return leg of Europa League qualifying. The Germans won the first leg in Slovakia 1-0.