Chasing a record-extending 10th European crown, Real were content to cede possession to the slick Bundesliga champions in the semi-final, first leg and created much the better chances with a series of trademark counter attacks.
Benzema's 19th-minute goal came from one such swift breakaway and set Real up for Tuesday’s return leg in Munich when they will be looking to avenge a reverse to Bayern at the same stage in the 2011-12 edition.
"At the start we were timid and we had some problems," Real coach Carlo Ancelotti told a news conference.
"In the second half, we had a bit more control," added the Italian, who is in his debut season in Spain.
"We were defending but we had some very good counter attacks.
"I am happy with everything, with the result and the commitment of the players, because the match was tough."
Ancelotti's side may, however, live to regret squandering two first-half chances that could have put the tie beyond Bayern’s reach.
Champions League top scorer Cristiano Ronaldo, back after injury, sliced a first-time shot high and wide in the 26th minute and Angel Di Maria blasted an angled effort over the crossbar when well placed four minutes before the break.
Bayern were thwarted time and again by a well organized Real defensive line and came closest to scoring late on when substitute Mario Goetze was denied by a brilliant save from Real captain and goalkeeper Iker Casillas.
It marked a losing return to Spain for Bayern coach Pep Guardiola, who mostly got the better of Real in four trophy-laden seasons in charge of their arch rivals Barcelona between 2008 and 2012 but suffered his first defeat at the Bernabeu.
"I did not want to have the typical German game of back and forth," Guardiola told German television broadcaster ZDF.
"I wanted a lot of possession and we managed that in part. But we did not finish our chances well," added the 43-year-old.