The overall tie finished 5-0 on aggregate in favour of the Italian side.
Nigerian striker Victor Osimhen scored a brace while Zielinski sealed the victory thanks to a 64th minute penalty.
Frankfurt managed just one shot on target for the entire match, with only 37 per cent possession.
Napoli’s first goal came just before halftime with a looping Osimhen header from Politano’s cross.
Osimhen’s second came in the 53rd minute as Di Lorenzo’s square ball allowed the Nigerian to tap into an empty net.
Napoli almost went 3-0 ahead with a shot from Khvicha Kvaratskhelia that was met with an excellent low save from Frankfurt keeper Kevin Trapp.
The third goal eventually came when Zielenski slotted home a spot kick straight down the middle.
The quarter final draw will occur at 10pm Friday, AEDT.
