They sealed a 2-1 home win over Eintracht Braunschweig with goals from Marco Reus and Jonas Hofmann.
The 21-year-old Hofmann grabbed the limelight from Dortmund's record-signing Henrikh Mkhitaryan, who made his debut after costing €27.5 million from Shakhtar Donetsk.
The Champions League runners-up are top the table on goal difference ahead of Bayern Munich and Bayer Leverkusen.
Hertha Berlin, who had been top of the league going into the weekend, could only manage a 2-2 draw at Nuremberg thanks to a late equaliser from Japan midfielder Hiroshi Kiyotake.
On Saturday, defending champions Bayern Munich laboured to a 1-0 win at Eintracht Frankfurt while both Hamburg and Schalke 04 suffered heavy defeats which left Leverkusen in second after their 1-0 win at VfB Stuttgart.
Croatia striker Mario Mandzukic gave Bayern the three points at Frankfurt
when he volleyed home a cross from Germany's Thomas Müller on 13 minutes.
It was a rare highlight in a below-par performance as Bayern failed to dominate, despite enjoying 70 percent possession, while Frankfurt captain Alex Meier had a goal ruled offside and a penalty appeal turned down in the dying stages.
Brazil midfielder Luiz Gustavo, who signed for Wolfsburg last week from Bayern after rejecting offers from Arsenal and Barcelona, made his debut in their 4-0 rout at home over Schalke 04.
Hamburg, meanwhile, were humiliated 5-1 at home by Hoffenheim as Brazilian striker Roberto Firmino ran riot, scoring twice and setting up the other three.
Mainz enjoyed a 2-1 win at Freiburg while Bremen picked up another win with
a 1-0 victory at home over Bavaria's Augsburg.
Borussia Mönchengladbach bounced back from their opening day defeat at
Bayern with a 3-0 win at home against Hanover 96.