Benzema clipped a Marcelo cross high into the net from close range in the 27th minute, the France forward’s fifth goal in this season’s ompetition, to maintain Real’s perfect record in the section with 12 points from four games.
It was the record 10-times European champions’ 12th win in a row in all competitions and followed their 3-0 success against Liverpool at Anfield last month.
“We have done our homework and we can now focus on La Liga, the King’s Cup and the Club World Cup,” Real captain and goalkeeper Iker Casillas said in an interview with Spanish television.
“We are very pleased,” added the Spain international, who was making a record 144th Champions League appearance.
“We have had some very tough and difficult matches recently and once we went 1-0 ahead we controlled the game.”
A major surprise was the fact that Cristiano Ronaldo failed to get on the scoresheet and he remains one goal short of the Champions League scoring record of 71 set by former Real and Schalke 04 forward Raul.
FC Basel are well placed to join Real in the knockout round after they beat Ludogorets 4-0 to move onto six points, with Liverpool and the Bulgarian champions on three each.
Real were close to full strength for the clash at a chilly and breezy Bernabeu, while Liverpool coach Brendan Rodgers made a host of changes from the team that lost to Newcastle United in the Premier League at the weekend.
Captain Steven Gerrard, Coutinho, Raheem Sterling, Jordan Henderson and Mario Balotelli were all on the bench, while Gareth Bale, who is coming back from injury, was among the Real substitutes.
Real had an early chance when James Rodriguez forced a good save from Simon Mignolet in the fourth minute before the visitors settled and started to play some neat football without threatening the home goal.
A mistake by Liverpool captain Martin Skrtel in the 10th minute gifted possession to Benzema and he set up Ronaldo, but Mignolet pulled off another fine stop to deny the Portuguese.
A well worked move yielded Real’s opening goal. Isco sent Marcelo clear on the left and his pinpoint cross was turned high into the net by Benzema as the Liverpool players appealed for a non-existent offside.
Liverpool failed to muster a shot in the first half to Real’s 13 and the European champions continued in the second period where they had left off with Ronaldo going close in the 49th minute.
Alberto Moreno had Liverpool’s first effort when he forced Casillas into a save in the 56th minute and Adam Lallana fired wide two minutes later.
Bale, who had replaced Rodriguez nine minutes earlier, turned a Marcelo cross onto the bar in the 71st and although the introduction of Sterling with about 20 minutes left gave Liverpool extra zip they did not come close to an equaliser.
“I knew what I was doing with the team selection and we are disappointed with the result but it was a good performance,” Liverpool coach Brendan Rogers, whose side host Chelsea in the Premier League on Saturday, said on UEFA.com.
“We showed great composure and a courage to want to play,” he added. (Reuters)