Eden Hazard was amongst those to make his debut for Los Blancos, but there was no Gareth Bale with the Wales international left out of the squad altogether amid the speculation surrounding his future at the club.
A bright start from Madrid saw Karim Benzema and Isco both have efforts in the first four minutes - the offside flag was raised on both occasions, but it was an early sign of the Spanish club's intent.
The German champions took the lead in the 15th minute, however, with Tolisso finding the back of the net at the second time of asking after seeing his first attempt blocked on the line by Marcelo.
Sanches then saw a goal-bound effort blocked following a quick break as Niko Kovac's side continued to cause issues on the counter-attack after a slow start.
Benzema was easily Madrid's most dangerous player in the first 30 minutes and the France international had another opportunity after breaking into the Bayern box, only for Neuer to make a smart save down low.
Courtois was also busy down the other end, however, with the Belgium international making a smart save to deny Thiago with both teams looking for early shots on goal.
There was not too much in the way of possession football from either side, which continued to create an open game. Indeed, Madrid had another chance to level in the 35th minute when Marco Asensio found himself inside the Bayern box, but the Spaniard's effort was blocked into the arms of Neuer.
Bayern's goalkeeper had to make another save to keep out a powerful Hazard drive five minutes before the end of the first half, before the resulting break saw Jann-Fiete Arp fire wide down the other end.
The final two opportunities of the first half came for Madrid through Benzema and Modric, but the former just failed to meet a brilliant Asensio cross before the latter saw his low attempt saved by Neuer.
A thoroughly entertaining opening 45 minutes produced an incredible 24 attempts in total, with both sides having a number of opportunities to add to Tolisso's strike.
Zidane changed his entire XI at the interval, with Luka Jovic, Ferland Mendy, Takefusa Kubo and Rodrygo Goes all coming in for their debuts, but Bale did not feature after being left out of the squad altogether.
Bayern were the team on the front foot in the early stages of the second period and Keylor Navas had to make a brilliant save to deny Tolisso just before the hour mark.
The Bundesliga giants doubled their advantage in the 67th minute, though, with Lewandowski doing brilliantly to free himself inside the Madrid box before picking out the bottom corner.
Gnabry then tested the reactions of Navas moments later as Kovac's team went in search of a third.
Gnabry was not to be denied moments later, though, with the former Arsenal attacker given the freedom of the Madrid box before converting past Navas to make it a quick-fire double in Houston.
Sarpreet Singh somehow fired wide of the Madrid goal 15 minutes from time with Bayern utterly dominant as the German champions continued to create chance after chance in the final third.
Bayern were reduced to 10 men in the 81st minute when substitute goalkeeper Ulreich picked up straight red card for bringing Rodrygo to the ground after the Brazilian had raced clear.
Rodrygo was soon back on his feet and picking out the top corner with a stunning free kick, though, as the summer arrival capped his first appearance for Los Blancos in style.
Singh thought that he had scored a fourth for Bayern late on, but the offside flag came to Madrid's rescue as an incredibly entertaining match ended with more drama.
Next up for Bayern is a clash against AC Milan in Kansas on Tuesday, while Madrid will face Arsenal in Maryland on the same night.
BAYERN MUNICH: Neuer (Ulreich 46'); Kimmich, Boateng, Martinez (Sule 46'), Alaba (Singh 73'); Tolisso (Zaiser 73', Hoffmann 82'), Sanches (Pavard 46'), Thiago (Goretzka 59'); Arp (Gnabry 46'), Muller (Lewandowski 46'), Coman (Davies 59')
REAL MADRID FIRST-HALF XI: Courtois; Carvajal, Ramos, Varane, Marcelo; Kroos, Modric, Isco; Asensio, Benzema, Hazard
REAL MADRID SECOND-HALF XI: Navas; Sanchez, De La Fuente, Nacho, Mendy; Kubo, Rodrygo, Seoane; Lucas, Jovic, Vinicius