Summer signing Afonso Moreira stole the show with two first-half goals on his debut, while Christian Kofane also found the net before the break.
After the interval, Victor Boniface struck twice, with Robert Andrich and Nathan Tella completing the scoring in the 70-minute contest.
Martinez handed opportunities to several young players, while World Cup participants and new signing Kennet Eichhorn were unavailable.
Moreira impressed throughout, combining his two goals with an energetic display on the left wing.
Leverkusen continue their pre-season schedule next weekend with a friendly against Kickers Offenbach before hosting an open training session at the BayArena.
