Bayern dominated possession in the semi-final, first leg at the Bernabeu without posing much of a threat to the home goal and Benzema’s 19th-minute effort means Real will have the advantage going into next week’s return in Munich.
Despite the victory, Real may live to regret not converting a couple of clear chances in the first half when Champions League top scorer Cristiano Ronaldo, back after injury, and Angel Di Maria both produced wasteful efforts.
Bayern almost equalised late on but Mario Goetze was denied by a brilliant Iker Casillas save.
It was 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.
With decorated Italian coach Carlo Ancelotti in his first season, Real have high hopes they can finally claim the elusive 10th European crown they have been chasing since their last triumph in 2002.
There was an electric atmosphere at their giant Bernabeu arena before kickoff and the home fans unfurled a huge banner proclaiming their status as “Kings of Europe”.
However, it was the current champions and five-times winners who bossed the early stages with the Real players clearly under instructions to sit back and try and hit Bayern on the break.
The opening goal came from exactly that scenario. Toni Kroos had a shot blocked in the Real penalty area and the home side picked up possession and poured forward.
Ronaldo played Fabio Coentrao in on the left and his low cross evaded the Bayern defence and found Benzema waiting at the far post to tap into an empty net.
Real were lifted by the goal and while Bayern were still enjoying long periods of fruitless possession the home side had two more clear chances on the breakaway.
Ronaldo sliced a shot high and wide when well placed in the 26th minute and Di Maria found space in the area four minutes before the break but blasted his effort over the bar.
Real were first to threaten in the second period thanks to an error in the Bayern defence and Ronaldo, back after knee and thigh muscle injuries, raced clear on the right and forced a fine diving save from Manuel Neuer with a low shot.
The Portugal captain has a record-equalling 14 goals in the Champions League this season and was clearly hungry to set a new best and Neuer again had to be alert when Ronaldo cracked a low shot towards the corner in the 68th.
Bayern huffed and puffed, with Arjen Robben and Franck Ribery probing down wither flank, but there was no way through the massed ranks of Real defenders.
The Bundesliga champions enjoyed a good late spell and Goetze might have done better when left unmarked 10 metres out but Casillas was equal to his shot.
In added time, Bayern claimed a penalty after Xabi Alonso dispossessed substitute Thomas Mueller when he was about to shoot but referee Howard Webb waved away their furious protests.
(Reporting by Iain Rogers, editing by Justin Palmer)