Bayern coach Niko Kovac was under pressure to deliver a convincing win after his side were knocked out of the Champions League in the last 16 by Liverpool last week, and his team responded with their 13th win in their last 14 league games.
The result saw Bayern move level with Borussia Dortmund on 60 points with eight games left, but the Bavarians top the table with a goal difference of +41 compared to Dortmund's +34.
Polish striker Lewandowski’s neat finish opened the scoring after three minutes and Coman almost doubled their advantage when his powerful angled shot came back off the post.
Bayern pulled away with two goals in five minutes before the interval, Rodriguez racing onto Leon Goretzka’s lay-off to fire home before Coman cut inside and curled a shot into the corner of the net from the edge of the box.
Rodriguez piled on the misery for Mainz six minutes into the second half when he notched his second goal of the day, before the on-loan Real Madrid midfielder completed his treble with a dinked finish after a defensive mix-up.
Teenage substitute Davies completed the rout with his first Bundesliga goal 20 minutes from time, leaving the visitors in 13th place on 30 points.
(Reporting by Alasdair Mackenzie; editing by Ken Ferris)
