After earning a 1-1 draw away to Finnish cup holders RoPS, the Greek side triumphed 4-2 on home soil to set up a two-legged clash with last season's seventh-placed Bundesliga outfit.
"Playing in the Europa League's a massive opportunity for us," enthused Mainz sporting director Christian Heidel. "We're really excited about it. Balancing domestic and European football will be a challenge, but that's part of the attraction."
The first-leg will take place on Thursday, 31 July at the Coface Arena, with the return fixture pencilled in for the following week. A place in the play-offs awaits the winners of the third-round tie, after which the group phase of the tournament gets under way.