Fernando Torres and Benayoun had chances to catch Madrid on the break but with eight minutes remaining it was the Israeli international who, unmarked, headed home Fabio Aurelio's free kick.
Liverpool boss Rafael Benitez was delighted with the result.
"We knew it was going to be very difficult," admitted Benitez. "They were winning games in a row so we knew they had a lot of confidence.
"We needed to work very hard, we had some chances and at the end from the free kick we scored a very good goal and without Gerrard and Torres in that second half the team was doing well.
"He (Torres) twisted his ankle in the first half and we were waiting but we could see that he wasn't fully fit and would be a risk for the next games.
"It's important in Europe not to concede but especially here because they've been scoring so many goals, but teamwork was very good.
"I was very pleased with the team's defending and also we were going forward and trying to score and at the end 0-1 is a very good result."