The Regionalliga Nord side stormed into a 2-0 lead with Germany Under-19 international Frahn scoring in the sixth minute and doubling the lead 11 minutes later.
Wolfsburg were level before the half hour mark with two goals in three minutes. Srdjan Lakic (25) pulled one back before veteran midfielder Hasan Salihamidzic equalised.
Frahn then completed his hat-trick on the stroke of half-time and Leipzig held on to pick up a memorable victory.
Stuttgart advanced after goals from Ermin Bicakcic (five) and Zdravko Kuzmanovic (51) saw win 2-1 at Wehen, a 28th minute Zlatko Janjic penalty proving to be only a consolation for the hosts.
Borussia Monchengladbach beat SSV Jahn Regensburg 3-1 to reach the second round. Martin Stanzl (14) and Marco Reus (22) put the Bundesliga side in control.
Tobias Schweinsteiger, older brother of Germany international Bastian, then pulled one back from the spot after 30 minutes before Igor De Camargo (70) wrapped up the win.
1860 Munich twice came from behind to win 3-2 at VfL Osnabruck after extra time. Gerrit Wegkamp (2) and Jan Mauersberger (34) gave the hosts the lead but Benjamin Lauth (11) and Kevin Volland (48) pulled 1860 level on both occasions before Lauth (106) scored the winner in extra time.
RW Essen recovered from a last-minute equaliser to beat Union Berlin 4-3 on penalties. Timo Brauer (22) and Benedikt Koep (71) put Essen 2-0 up before Patrick Zoundi (82) and Simon Terodde (90) took the game to extra time. Neither side could find a winner before Essen held their nerve in the shootout.
Erzgebirge Aue needed extra time to beat FC Saarbrucken 3-1 with Jan Hochscheidt (100) and Mike Konnecke (119) grabbing the vital goals.
Thomas Paulus had given Erzgebirge the lead through a 35th minute penalty but Mark Lerandy (79) levelled for Saarbrucken.