The Spanish giants remain on course to complete La Decima and become the first club to take their European Cup tally into double figures after Benzema's first-half strike at the Bernabeu earned them a precious lead in the tie.
Carlo Ancelotti's men were on the back foot in terms of possession for much of Wednesday's game, but they showcased their clinical side to give the Champions League holders plenty of work to do to progress to this year's showpiece.
Benzema's goal came against the run of play but got Real off to a strong start as the French striker tapped home the opener from close range 19 minutes in.
Despite the return of Cristiano Ronaldo from injury, Real's forward momentum was limited for long spells but they were able to soak up any Bayern pressure.
Bayern also struggled to forge openings, until Arjen Robben flashed an effort wide of Iker Casillas' right-hand post after 13 minutes.
Toni Kroos' shot was then blocked by Pepe before Real broke at pace, allowing Ronaldo to find Fabio Coentrao down the left.
And when his cross evaded Dante, Jerome Boateng and Neuer, Benzema was left with the simplest of tasks to finish and put the hosts ahead.
Ronaldo had a glorious opportunity to double the advantage soon afterwards, blazing Benzema's pass over the crossbar, as Bayern struggled to regain their early rhythm.
David Alaba and Franck Ribery went close to threatening a response but they were quickly dealt with, before Angel Di Maria fired over from a tight angle as the game opened up again in the latter stages of the first half.
In a nervy finish, Mario Gotze was denied by a smart Casillas stop before Bayern's appeals for a penalty following a challenge by Xabi Alonso on Thomas Muller were waved away by referee Howard Webb.
