The hosts struggled to break down a resilient Bochum in the opening 20 minutes, but that soon changed with Takashi Inui at the heart of their good play.
He broke the deadlock in the 24th minute from the spot and then had a huge say in the second goal just two minutes later.
The Japanese timed his pass to Stefan Aigner perfectly, with the striker slotting the ball home with ease.
Frankfurt's dominance continued into the second half and they should have wrapped up the match just five minutes after the break, but Vaclav Kadlec headed wide when he should have done better.
Bochum finally came into the game after the break, but most of their efforts were from range and they remained unable to test Kevin Trapp and the hosts comfortably saw out the rest of the game.
Elsewhere in the DFB-Pokal, FSV Frankfurt lost 2-0 at home to Ingolstadt, Hertha Berlin were beaten by 2. Bundesliga side Kaiserslautern 3-1 and Saarbrucken beat Paderborn 2-1.