Brazilian playmaker Caio opened the scoring for Michael Skibbe's side in the first minute, dispossessing Aachen defender Seyi Olajenbesi before finishing at the second attempt after his first effort was blocked. Only five minutes had passed when Greek striker Nikos Liberopoulos doubled the lead, heading an Aleksandar Vasoski header over the line.
Half-time lead
Babacar Gueye pulled Aachen back into the game, nodding in after seeing his initial header saved superbly by Frankfurt keeper Oka Nikolov, but the visitors' joy was short-lived as a Lukasz Szukala own-goal on the stroke of half time restored the hosts' two-goal lead.
Down, but not out
Liberopoulos grabbed his second and Frankfurt's fourth five minutes after the restart, finishing at the far post after a low cross from the right by Selim Teber. Alexander Meier then seemingly put the game beyond the realms of the comeback, profiting from the remnants of a long-range Caio effort.
Aachen were down, but certainly not out, and began what appeared like it might be one of the great all-time comebacks when Benjamin Auer finished coolly past Nikolov following a Herve Oussalé pass. Seven minutes later and the deficit was reduced to two, Auer again the scorer from a Timo Achenbach cross from the left.
Tense finish
With just three minutes remaining, Gueye pulled another one back to set up a tense finale, but a penalty in the dying seconds from Teber rounded off the scoring at a perfect ten and ensured Frankfurt's progression into round three.
Aachen can take solace from their team's spirited fightback and goalscoring display, though new coach Michael Krüger will surely swap such entertaining football for a run of 2. Bundesliga victories from hereon in.