We started both halves well, Erik Lamela blasting over our best chance early on before Real Madrid's best spell and opening goal in the first half.
The second period was a quieter affair with both teams happy to keep hold of possession in the Munich heat and Bale's goal came out of nothing to secure victory for the La Liga giants.
We will now play either Bayern Munich or AC Milan in the third/fourth place match on Wednesday night, kick-off 5.15pm (UK time).
A full house at the Allianz Arena greeted us as we stepped out in our new purple third kit for the first time.
With the start of the Premier League season just four days away, there was plenty to play for in Munich with places up for grabs for the opening day trip to Old Trafford.
Dele Alli made his first start and impressed in central midfield with Kevin Wimmer initially partnering Toby Alderweireld at centre-half and Lamela back for his first pre-season action. Mousa Dembele, Michel Vorm, Kyle Walker, Alderweireld and Danny Rose went on to complete 90 minutes.
It was a lively start from both sides as first Lamela squandered a glorious chance to break the deadlock from a Walker cut-back.
Jese was the danger man for Madrid as he rattled Vorm’s crossbar early on with a snapshot on the angle before bringing the best out of the Dutch goalkeeper two minutes later with a curling effort.
It was hot and humid but there was barely time to draw breath as the game ebbed and flowed with the pace and intensity of a league fixture early on.
Christian Eriksen was next to go close with 15 minutes on the clock. Bavaria is famed for its alpine skiing and the Danish midfielder gave a perfect demonstration of the skills required for the sport when he slalomed in from the left and hit a dipping shot that Kiko Casilla scrambled clear with his legs.
The pace would calm down but the chances kept coming as Vorm pulled off a world class save as the half wore on. Ex-Spurs man Luka Modric let fly from distance with a shot that cannoned off of Kevin Wimmer, wrong-footing Vorm in the process. The keeper showed tremendous athleticism, though, to change direction and palm the shot away.
The deadlock was broken soon after when Isco crossed perfectly from the left for James to head home as he found space between our defensive line.
It was relatively even on the balance of play going into the second period as Eriksen blazed one over early on in a tweaked midfield as the impressive Alli switched to a more advanced role behind Harry Kane.
Nacer Chadli came on at the interval and good work from Rose saw him find an opening but Casilla did well to beat his shot away.
We were enjoying our best spell of the game as both sides rung the changes which somewhat stifled the flow of the match as chances remained at a premium.
Our former star Bale had been quiet but with just over 10 minutes to go he put the game beyond us. The forward picked the pocket of Tom Carroll before hitting a rasping shot that bounced awkwardly in front of Vorm and into the bottom corner.
Real Madrid: Casilla, Varane, Ramos (c), Kroos (Casemiro 45), James (Vazquez 45), Bale (Mayoral 82), Marcelo (Arbeloa 59), Modric (Illara 59), Jese (Cheryshev 59), Isco, Danilo. Substitutes (not used): Navas, Pepe, Nacho, Carvajal, Yanez, Asensio, Odegaard.
Spurs: Vorm, Walker, Rose, Alderweireld, Lamela (Chadli 45), Dier (Bentaleb 45), Kane (c) (Onomah 86), Dembele, Alli (Winks 68), Eriksen (Carroll 68), Wimmer (Vertonghen 45). Substitutes (not used): McGee (GK), Trippier, Fazio, Davies, Mason.
Goals: Real Madrid - James 36, Bale 78.