Berliner played with a zip and purpose that caught their visitors, 11th in the Bundesliga last season, off guard.
Metin Cakmak opened the scoring after two minutes following a mix-up in the Hoffenheim defence, with Justin Gerlach finishing off a neat counter-attacking move to double the lead just past the half-hour mark.
Kevin Kruschke made it 3-0 before halftime, with Cakmak getting his second, and Berliner's fourth, early in the second half.
Holders Borussia Dortmund began their defence of the competition with a straightforward 3-0 win at fourth-tier side FC Oberneuland.
Dortmund took the lead after 10 minutes with a Marco Reus goal, before Jakub Blaszczykowski doubled their advantage and Ivan Perisic grabbed a third late on in the second half.
Bundesliga clubs Bayer Leverkusen (4-0 at Carl Zeiss Jena), SC Freiburg (2-1 at Viktoria Hamburg), VfB Stuttgart (5-0 at SV Falkensee-Finkenkrug) and Borussia Moenchengladbach (2-0 at Alemannia Aachen) all made it through without too many problems.
- Borussia Dortmund