Frankfurt are fifth on 46 points, level with fourth-placed Schalke 04 who take on Hamburg SV later on Sunday and could tighten their hold on the spot that leads to the Champions League qualifying rounds with three games left.
After a dull first half, the home fans had briefly something to celebrate until Andreas Ivanschitz's effort was ruled off side.
Eintracht coach Armin Veh threw two more strikers, Olivier Occean and Srdjan Lakic, into the mix after an hour but the move failed to pay off.
Mainz, who were without injured striker Adam Szalai, drop to 10th on 40, five points off the Europa League spots.
Already crowned champions, Bayern Munich also set a Bundesliga record for most points when they moved on to 84 following their 1-0 victory over Freiburg on Saturday.
Fellow Champions League semi-finalists Borussia Dortmund deployed a second-string team to beat Fortuna Dusseldorf 2-1 and stay eight points clear in second place.
- Sports & Recreation
- Andreas Ivanschitz
- Olivier Occean
- Srdjan Lakic
- Hamburg SV