A new era up top for Bayern had former Liverpool star Sadio Mane debuting following his arrival in the off-season, with record scorer Robert Lewandowski having left for FC Barcelona.
Bayern had no problems settling as misplaced possession from Konrad Lainer on 14 minutes alerted Jamal Musiala, who pounced and went on to give the all-conquering Bundesliga champions the lead.
The hosts seemed to have clawed back minutes later through Christopher Nkunku following a through ball, but it was called for offside.
Julian Nagelsmann’s side instead doubled their tally seconds from the half-hour mark when Serge Gnabry’s ball picked out Mane, who took charge and grabbed his first for his new club.
Bayern launched more threats towards halftime and snatched a third after Benjamin Pavard slammed a ball from Musiala’s corner-kick into the bottom of the net.
The Red Bulls looked for a renewed spell minutes in the second period and initiated two substitutions in Andre Silva for Emil Forsberg and Dani Olmo ahead of Kevin Kampl.
Leipzig did carve out a lifeline on 59 minutes where a delivery from another corner had defender Marcel Halstenberg head past Bayern goalkeeper Manuel Neuer and into the net.
The Bavarians restored their advantage though after Gnabry retrieved possession and applied a close-range finish six minutes later, as new signing Ryan Gravenberch entered for his debut.
However, Leipzig didn’t give up and bagged a second in the remaining 12 minutes when Nkunku converted from the penalty-spot after Pavard fouled Olmo in the area.
A nervy finish was on the cards with a minute to go as Olmo picked up a pass from Szoboszlai and finished off smartly.
Bayern though didn’t crack and found a fifth in the dying second through Leroy Sane following a ball from Alphonso Davies, as the clash concluded in favour of the Bavarians.