But the reigning champions, seeking a fourth straight title, were given a major scare by the only team left in the competition who had to come through qualifying.
Four-time winners Ajax, in the knockout stages for the first time in 13 years, dominated for long spells.
In a vibrant display they hit the woodwork, tested Thibaut Courtois frequently and had a goal ruled out by the video assistant referee before Benzema struck.
Hakim Ziyech then equalised for Ajax, only for substitute Asensio to grab the winner three minutes from the end.
Ben Hayward assesses the key talking points in Amsterdam…
Benzema is a guarantee in the Champions League
Benzema’s goal for Real Madrid tonight was his 60th in the Champions League, which sees him draw level with Ruud van Nistelrooy on the all-time scorers list in the continental competition.
The French forward, a four-time winner of the Champions League with Real, is now behind only Raul (71), Lionel Messi (106) and Cristiano Ronaldo (122).
He was withdrawn with 17 minutes left after suffering a back problem earlier in the week and Madrid coach Santiago Solari will want to keep him fresh for the big games ahead.
Vinicius on song, but Bale misses chance
Vinicius Junior has been lighting up La Liga and the Copa del Rey already and now, at the age of 18, he is doing it in the Champions League as well.
It was the Brazilian’s brilliant run which set up Benzema for the all-important opening goal and his pace will cause problems for any team in this competition.
Gareth Bale had a more difficult night.
The Welsh winger helped out a lot in defence, but failed to make much of an impact in an attacking capacity and hesitated once in the first half when he had a good opportunity to shoot from the edge of the box.
He was substituted just after an hour and on this form, he may not start again soon in a big game.
De Jong looks like a Barcelona player already
Barcelona fans will have been impressed with Frenkie de Jong, who will move to the Catalan club in the summer.
The midfielder showed plenty os skills as he moved the ball around in tight spaces and sprayed passes around to his team-mates.
He is not the finished article, but at the age of 21, he already looks like the kind of player who will fit in seamlessly at Camp Nou.
He was also fouled in the lead-up to Madrid’s second goal by Lucas Vazquez and Ajax were unfortunate the move was allowed to continue.