The Frenchman was on hand to turn home Fabio Coentrao's cross on 19 minutes and Madrid's advantage could have been even greater had Cristiano Ronaldo and Angel di Maria not missed fine chances before the break.
Bayern had the overwhelming majority of possession but failed to convert it into many sights of goal as Iker Casillas' save from Mario Goetze five minutes from time was the only significant stop the Spanish captain was forced into all evening.
"We played with a lot of personality, we had a lot of possession we will have to improve in Munich, but I am very proud," said Bayern boss Pep Guardiola.
"I have experience of how difficult it is to come here and play at the Bernabeu but I congratulate them because they won and if they own it is because they played better."
Real coach Carlo Ancelotti, meanwhile, hailed the effort of his players to keep out Bayern for 90 minutes despite their lack of possession.
"When you have the combination of quality players and sacrifice that is all you can ask for.
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