Winger Karim Bellarabi took nine seconds to score the opener for the visitors with Dortmund below par despite the return of Marco Reus after an injury that saw him miss the World Cup.
Stefan Kiessling scored the visitors' second goal in stoppage time to secure victory with Bellarabi pouncing on an Erik Durm mistake to set up the forward.
Dortmund coach Juergen Klopp, who set a club record for being in charge for a seventh straight season, was missing eight players through injury and it showed.
Fellow Champions League competitors Leverkusen, buoyed by their early goal, looked livelier throughout and confirmed their good form after also winning their Champions League first leg qualifier in Copenhagen midweek.
The hosts, who had won their previous three season openers, and also clinched the German Super Cup against Bayern Munich earlier this month, were far too slow and had problems dealing with Leverkusen's pressing.
Leverkusen central defender Omer Toprak allowed little at the back while the hugely talented Hakan Calhanoglu, signed from Hamburg SV for 15 million euros ($19.86 million), was a constant source of danger with long crosses and set pieces.
Dortmund's best chance came six minutes from time but keeper Bernd Leno spectacularly saved Matthias Ginter's header to give coach Roger Schmidt a winning start on the Leverkusen bench.
Hanover 96 stunned Schalke 04 with two goals in three minutes to win their Bundesliga opener 2-1 and pile pressure on Schalke coach Jens Keller following their embarrassing German Cup exit earlier this week.
Dutch striker Klaas-Jan Huntelaar completed a quick break for the visitors two minutes after the restart to give Schalke the lead and raise hopes of banishing Monday's first round defeat by third-tier Dynamo Dresden.
Hanover, who had Germany keeper Ron-Robert Zieler to thank for keeping them in the game, levelled through Edgar Prib in the 67th after he connected with a Leonardo Bittencourt cross in their first real chance of the game.
New arrival Joselu's thundering drive in the 70th completed an unexpected comeback for Hanover, with Schalke having only themselves to blame for failing to hold on to their lead.
Hoffenheim also got off to a winning league start after scoring twice in two minutes through new signing Adam Szalai and Tarik Elyounoussi to beat Augsburg 2-0.
Hertha Berlin also took a two-goal lead with a brace from Julian Schieber but squandered it in the second half to settle for a 2-2 draw with visitors Werder Bremen.
Eintracht Frankfurt gave new coach Thomas Schaaf a winning debut after edging Freiburg 1-0 courtesy of a first half Haris Seferovic strike.
Hamburg SV, who needed a relegation playoff to stay up last season, drew 0-0 with promoted Cologne.
Champions Bayern Munich made a winning start to their league season, edging past VfL Wolfsburg 2-1 on Friday.