Mane, who scored in Bayern's 3-0 midweek win at Barcelona in the Champions League, also missed a penalty. Serge Gnabry, Jamal Musiala and Leon Goretzka were also on target for Bayern along with substitute Mathys Tel and Eric Maxim Choupo-Moting.
The champions went two points clear at the top of the league with 25. Mainz drop to eighth on 18. Borussia Dortmund climbed to third on 22 following their 2-1 win at Eintracht Frankfurt.
"It is always great to see six different scorers because it means that six players will boost their confidence," said Bayern coach Julian Nagelsmann.
"Sadio has had a good development in the last couple of weeks. He did it well today like he did in Barcelona and I hope he will keep on like this for the next few weeks."
Bayern powered into an early lead with Gnabry completing a quick passing move in the fifth minute but Mainz moved instantly forward, with Jonathan Burkardt repeatedly testing Bayern goalkeeper Sven Ulreich.
It was Bayern, however, who scored again with Musiala threading in a shot to finish off another quick Bayern move.
Musiala, a firm candidate for Germany's World Cup squad, has now scored seven league goals, as many as Mane, and set up another four.
Mainz came agonisingly close to pulling back a goal when Burkardt rattled the crossbar with a shot and Lee Jae-sung thundered the rebound on to the post in the 31st.
Mane did much better on his rebound effort a little later, slotting in after Mainz's Robin Zentner had parried his penalty.
Mainz, who had won their previous three games in all competitions, bagged a deserved goal in first-half stoppage time when Widmer headed in from a corner after Ulreich had saved a spot kick to deny Burkardt.
Bayern, who also hit the woodwork with Choupo-Moting and Musiala in the second half, did not let up and Mane curled in a superb cross in the 58th for Goretzka to head in. Two more Bayern goals either side of Ingvartsen's effort completed the rout.