Lukas Klostermann put third-placed Leipzig in control with two first-half goals, tapping in from Timo Werner's pass after 20 minutes and then clipping a neat finish over Florian Mueller 12 minutes later.
Karim Onisiwo pulled one back with a shot on the turn before halftime but Werner restored Leipzig's two-goal lead four minutes after the break.
Moussa Niakhate pulled one back from a corner and his fellow Frenchman Jean Philippe Mateta levelled with seven minutes left although Leipzig then missed three chances to grab a winner.
Leipzig, already qualified for the Champions League next season, have 65 points, six behind leaders Bayern Munich, and two games left to play while Mainz are a comfortable 12th.
(Writing by Brian Homewood, editing by Pritha Sarkar)
