Dortmund made two changes from the DFB-Pokal final win over RB Leipzig, as Thomas Meunier and Giovanni Reyna were recalled while Erling Haaland was fit again to start.
The visitors were on the front foot early on and Raphael Guerreiro gave them the lead in the 23rd minute with a curling strike into the far post after he was teed up by Jadon Sancho.
BVB were opening spaces going all out in attack and they were nearly punished six minutes before the break after Karim Onisiwo broke through on goal but he looped his strike wide.
Marco Reus eventually doubled the lead for Edin Terzic's charges just before the break with a side-footed finish inside the six-yard box after a cut-back by Sanco.
Mainz had a bright start in the second stanza, as Onisiwo and Mousa Niakhate both came close to pulling a goal back four minutes from the break but were denied by shot-stopper Roman Burki.
The hosts kept on putting Dortmund under pressure and Danny Latza also came close in the 64th minute with a looping strike inside the box that was parried over the bar by Burki.
Bo Svensson made a double change in the last 18 minutes, as Adam Szalai replaced Onisiwo upfront while Kevin Stoger came on for Jean-Paul Boetius in midfield, both for fresh legs.
BVB were waiting to pounce on counter-attacks and Julian Brandt killed off the game with the third goal in the last ten minutes, scoring into an empty net after rounding goalkeeper Finn Dahmen from Haaland's through ball.
Robin Quaison got a consolation goal for Mainz in stoppage time from the penalty spot, as Dortmund moved up to third on the log, four points clear of fifth-placed Eintracht Frankfurt, with only one last round of matches remaining.