There were few chances early on as the defending champions tried to control possession, while an Angel di Maria run for the hosts was blocked by David Alaba.
The visitors came close to opening the scoring after a quarter of an hour when Arjen Robben created some space on the edge of the box before sending the ball towards goal, but his effort was off target.
Real were able to capitalise just a few minutes later when Fabio Coentrao picked out Benzema with a low cross, giving the striker a simple tap-in from close range.
Cristiano Ronaldo almost doubled their lead shortly after as he tried to head in from a Di Maria delivery, but his finish went straight into the hands of Manuel Neuer.
The Bundesliga champions had a couple of half-chances shortly before the break, but Robben saw his effort blocked before Pepe cleared a Franck Ribery cross.
Di Maria had another chance to add the hosts' second just before the half-time whistle as he found himself unmarked inside the box, but he sliced his shot high and wide to leave the Spanish side just one goal up at the break.