Zinedine Zidane opted to start with Lucas Vazquez and Isco, which saw Gareth Bale and Karim Benzema dropped to the bench.
The Bavarians were dealt a blow early on as talisman Arjen Robben picked up an injury in the ninth minute and had to be replaced by Thiago Alcantara.
Los Blancos were seeing less of the ball after 15 minutes, although the home side lacked penetration in the final third.
However, Joshua Kimmich broke the deadlock in the 28th minute for Jupp Heynckes’s charges with a strike at the near post following a through-ball from James Rodriguez.
Heynckes was forced into another substitution in the 35th minute as Jerome Boateng also picked up an injury and was replaced by Niklas Sule.
The Bavarians were on top of the match regardless and looked in control, while the visitors appeared shocked.
A minute before the break, though, Marcelo found the equaliser for Zinedine Zidane’s troops with a spectacular half-volley, 1-1.
Madrid came back a better side in the second stanza and ventured forward with much more purpose and intent.
Asensio gave Zidane’s men the lead three minutes before the hour mark with a cool finish on a counter-attack after he was set up by Lucas Vazquez, 1-2.
The hosts had a strong penalty appeal in the 68th minute after Thomas Muller appeared to have been brought down inside the box but the referee saw things differently and waved away the appeals.
Cristiano Ronaldo had a ball in the back of the net for Madrid with 15 minutes remaining but he was adjudged to have controlled the ball with his arm before firing in and the goal was ruled out.
However, Madrid still did enough to give themselves the advantage ahead of the return leg at the Santiago Bernabeu next week.