The visitors dominated possession in the early stages without really creating anything of note in front of goal and it was Madrid who took the lead after a swift counter-attack down the left.
Cristiano Ronaldo, who had recovered from a hamstring injury to return to the side, fed Fabio Coentrao inside the area and the full-back was able to cut it across goal where Benzema was waiting to slot it into an empty net with ease.
Bayern soon regained their rhythm and had their hosts pegged back, but it was again Carlo Ancelotti's side who had the better sights of goal as Ronaldo and Angel Di Maria both blazed over the bar from good positions.
After the break, Ronaldo twice forced Manuel Neuer into making smart saves, while Philipp Lahm could only poke the ball into the side-netting after bursting into the area.
Thomas Muller saw his effort deflected inches wide of the post after Raphael Varane's block, and Mario Gotze was denied by a smart save from Iker Casillas as the hosts stood firm to take a 1-0 advantage to the Allianz Arena on Tuesday, April 29.
Gareth Bale, who had been suffering from flu, began on the bench, while Bayern's two most expensive players, Javi Martinez and Gotze, were also substitutes.
The Bernabeu was rocking at the start for Real's fourth consecutive semi-final, but soon quietened down as Bayern took full control of the ball.
Pep Guardiola's side enjoyed 85 per cent of possession in the opening 20 minutes, but Madrid managed just fine without the ball, limiting their opponents to a shot by Arjen Robben that was deflected wide, and a soft effort by Bastian Schweinsteiger which Casillas saved comfortably.
Madrid had barely set foot in Bayern's area up until then but took the lead with their first attack. Bayern lost possession in Madrid's half and Ronaldo quickly released Coentrao down the left - and the defender pulled the ball back for Benzema to slam home from four yards out.
Di Maria tested Neuer a moment later, before Ronaldo squandered a glorious chance to double the lead. The Portuguese forward blazed over from inside the area when Benzema rolled the ball across to him from the left, one of few areas Bayern looked vulnerable in.
Madrid's next chance fell to Di Maria, who arrived at the far post to get on the end of an Isco cross, but he shot well over the bar with the outside of his boot. The Argentinian winger then frustrated the home crowd by trying to play in Ronaldo with a backheel, misplacing the pass.
At the other end, Lahm hit the side-netting and Robben's shot was blocked by Alonso.
Ronaldo gave Bayern another fright at the start of the first half when he tried to beat Neuer from a tight angle at his far post after a poor pass by David Alaba but the goalkeeper palmed the shot away for a corner.
Robben was Bayern's most adventurous attacker. He attempted a cross into the box that was swatted away by Casillas, then marauded through midfield but failed to trouble the Madrid goalkeeper with a soft effort.
Ronaldo then attempted to catch Neuer off his guard from the edge of the area, but the goalkeeper parried.
With six minutes remaining, the German's opposite number Casillas made the only decisive intervention he needed to, repelling substitute Gotze's strike from inside the area.
Bale caused Bayern problems after replacing Ronaldo - who did not look fully recovered from his fitness problems - but sent his only chance into the side-netting.
Real were hanging on towards the end and survived Bayern's appeals when Muller went down in the area - referee Howard Webb was unimpressed.