Before the match, FC Bayern Munich coach Pep Guardiola had warned that Real were the world's best side on the break and even though Cristiano Ronaldo and Gareth Bale were only half-fit, they terrorised the German champions' backline with their surging runs.
The duo should be in prime condition for next week's return Champions League semi-final leg at the Allianz Arena, where Real will hope to enjoy more success on the counter-attack and book a first final appearance for 12 years.
"It wasn't a case of him (Ronaldo) holding back but he wasn't 100 percent. He did few full-out sprints but for us the most important thing was that he played. He worked hard to be there and we are happy," Real coach Carlo Ancelotti told reporters after the win at the Bernabeu.
Ronaldo had not played since the beginning of April due to knee and hamstring problems and the Italian took him off for the final 20 minutes, replacing him with Bale, who had been suffering from a heavy cold all week.
"The substitution was a decision that we took before the game as the injury risk was higher after an hour of the game because the muscles would be tired," Ancelotti added.
FC Bayern Munich Domination
"It worked out fine and it was normal that after 20 days out that you are not 100 percent but he gave his all and will be better next Tuesday as will Bale."
FC Bayern Munich's early domination had looked ominous for the hosts but with the German side unable to fashion clear-cut chances, Real's quick breaks posed a far bigger threat to visiting fullbacks David Alaba and Rafinha pushing up the pitch.
By contrast, Real's own fullbacks Daniel Carvajal and Fabio Coentrao were regularly able to cause problems, getting forward frequently with the latter setting up Karim Benzema for the only goal of the match in the 19th minute.
"We had clear chances because this team is formidable on the break. It is normal that against FC Bayern Munich you counter-attack more and to do that you have to defend well," Ancelotti said.
"The higher up the pitch that you defend the better, and in the second half the pressure on us was less," he added.
"I don't like the other team having the ball but obviously you can't have it all the time and FC Bayern Munich have a clear philosophy.
"Now the second leg will be difficult. We have to play with confidence and be motivated. Anything can still happen in Munich."