Willock, 20, one of seven changes by Arsenal manager Unai Emery to the team which started Sunday's 2-2 draw at Watford, gave the Gunners a first-half lead after a deflection off a Frankfurt player.
Eighteen-year-old Saka and Pierre-Emerick Aubameyang grabbed late goals as Frankfurt were reduced to 10 men for the final 11 minutes when midfielder Dominik Kohr was shown a second yellow card for fouling Saka.
"Everybody can be happy and continuing in this competition is important, so it was good to get a good win, especially away from home," said Emery.