Joshua Kimmich had put the home side in front, but Marcelo equalised before the interval against the run of play.
Asensio then came on after the break and Lukas Vazquez set up the 22-year-old to claim a second away goal for Madrid 12 minutes into the second half.
The result puts the two-time defending champions in a favourable position before the second leg in Madrid next Tuesday, though Zinedine Zidane's side will be wary after conceding three goals at home to Juventus in the previous round.
Cristiano Ronaldo was held scoreless for the first time in the competition this season.
The Portuguese star had an effort ruled out in the second half for using his arm to control the ball.
Bayern, chasing a treble in Jupp Heynckes' last season in charge, was hoping to make up for last year's quarter-final exit to Madrid, and for the Spanish side's 5-0 aggregate win at the same stage in 2014.
Rafinha had the first shot on goal in the 19th minute after a cautious start from the visitors, who started with both Gareth Bale and Karim Benzema on the bench.
Madrid started to settle midway through the half before Kimmich struck.
James Rodriguez played the right-back through as Bayern created a three-on-two. Perhaps expecting a cross, Navas was surprised when Kimmich let fly to score inside the far corner.
Buoyed by the goal, Bayern's players suddenly found spaces but Ribery wasted a good opportunity to double the lead.
Instead, Marcelo levelled the score shortly before the break.
Bayern missed more chances before the interval, when Asensio came on for Isco to change the course of the game.
After Bayern turned the ball over in midfield, Vazquez and Asensio played a one- two before the substitute coolly dispatched the ball past Sven Ulreich.
Reuters
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