New signing Marcel Sabitzer scored on his competitive debut for Borussia Dortmund in a 6-1 victory over Schott Mainz in the first round of the German Cup on Saturday.

Five-time winners Dortmund went into the game without several key players.

Karim Adeyemi, Giovanni Reyna, Nico Schlotterbeck and goalkeeper Gregor Kobel were among the injured absentees, but Dortmund were never likely to encounter a problem against the team from the German fifth tier.

Sabitzer, a 19-million-euro ($20.8 million) acquisition from Bayern Munich this summer, premiered for the Black and Yellows, and made an impression in this gentle early-season test for Edin Terzic's side.

But it was striker Sebastien Haller who broke the deadlock in the 22nd minute, meeting Julian Brandt's cross from the left with a bullet header that flew past home goalkeeper Tim Hansen.

The lively Brandt got himself on the scoresheet two minutes later, converting Donyell Malen's cross from close range to put the 2021 winners in cruise control.

With Dortmund coasting, Schott Mainz briefly caused a stir, halving Dortmund's advantage through Nils Gans, who pounced from close range after Mats Hummels was wrong-footed at a free-kick.

But no sooner had Schott Mainz finished celebrating, Dortmund re-established their two-goal cushion through Haller, who brought free signing Ramy Bensebaini's cross under his spell and showed neat feet to slot home from close range for his second and Dortmund's third.

Former RB Leipzig midfielder Sabitzer, who spent the second half of last season on loan at Manchester United, got his goal shortly before the hour mark, drilling in a low rebound after good work by Marco Reus.

Malen added a fifth in the 80th minute and Youssoufa Moukoko came off the bench to put the gloss on the win with Dortmund's sixth.

Elsewhere, Bayer Leverkusen were also in ruthless mood, scoring eight without reply against fourth-tier Teutonia Ottensen, including a debut goal for new signing Jonas Hofmann.

There was also a comfortable win for Bundesliga side Stuttgart, who won 4-0 at TSG Balingen.

In the biggest shock of the day, Viktoria Cologne's Donny Bogicevic scored a 95th-minute winner to complete a stunning 3-2 victory for the third-tier team, knocking out 10-man Bundesliga club Werder Bremen.

"This is very hard to get your head around," Bremen coach Ole Werner told Sky Germany.

"Things have gone very bitterly for us today, right from the start. A lot of it was our own fault but the red card was far too easy.

"But we have to look at ourselves and make sure we don't lose in the other competitions."

Bremen begin their Bundesliga campaign on Friday, at home to champions Bayern Munich.