Julian Nagelsmann's side is just a point clear at the Bundesliga summit after three successive 1-1 draws, but it ended its winless run with a dominant showing at MEWA Arena on Thursday (AEDT).
Manchester City loanee Joao Cancelo assisted Choupo-Moting's opener just 17 minutes into his debut, before the striker teed up Leroy Sane on the stroke of half-time after Jamal Musiala's 30th-minute strike.
Substitute Alphonso Davies sealed the victory in the second half prior to Alexander Hack being dismissed late on, as Bayern picked up a first win of 2023 to remain on course for a first DFB-Pokal triumph since 2020.
Mainz did not heed the early warning signs against a dominant Bayern and were punished as Choupo-Moting expertly volleyed Cancelo's right-wing centre past Finn Dahmen at the far post.
Musiala doubled the visitor's advantage with a pinpoint left-footed finish into the bottom-right corner after Thomas Muller's delicate pass.
Joshua Kimmich then curled a free-kick from a tight angle against the left post, before Sane calmly finished from Choupo-Moting's throughball as a rampant Bayern ran riot in the first half.
Hack cleared Muller's deflected attempt off the line after the interval, while Anthony Caci whipped a rare Mainz chance narrowly wide at the other end.
Davies nodded Kimmich's right-wing cross past Dahmen for Bayern's fourth, before Hack was shown a second yellow card for a needless foul on Musiala as Bayern eased to victory.
