Borussia Moenchengladbach and VfB Stuttgart, the other Bundesliga teams playing on Friday, beat third division opposition while former German champions Rot-Weiss Essen, now in the fourth tier, beat second division Union Berlin on penalties.
The first round is a potential minefield for Bundesliga and second division clubs as the seeding system forces them to play one-leg ties away to lower division opponents.
Playing before the league has started adds to the chances of top teams being caught unprepared.
Daniel Frahn scored a hat-trick for RB Leipzig, who were known as SSV Makranstaedt until 2009 when the Red Bull energy drinks manufacturer bought the playing licence and changed the name.
Frahn opened his account in the sixth minute when Wolfsburg failed to clear a corner and scored again from close range 11 minutes later before a crowd of more than 30,000.
Wolfsburg, who pulled off a dramatic rescue act under Felix Magath to escaple relegation last season, were level before the half hour when Srdjan Lakic and Hasan Salihamidzic scored in a three-minute spell.
But Frahn struck again on the stroke of halftime when he headed the third and decisive goal.
Moenchengladbach won 3-1 at Regensburg while Stuttgart overcame Wehen Wiesbaden 2-1.
Rot-Weiss, who were German champions back in 1955 but have suffered from numerous financial problems in the last few years, took a 2-0 lead against Union Berlin, who hit back with two goals in the last 10 minutes.
Not to be denied, the hosts won 4-3 on penalties.
