With a quarter of the match played the visitors finally started to show just why they have made it through to at least the semi-finals seven years running, getting off the mark through a fine Benzema strike.
In temporary coach Santiago Solari's first Champions League game in charge Real began slowly but were out of sight before halftime after a clinical masterclass of finishing.
Real Madrid has undergone significant change since its last Champions League outing, a 2-1 win over Plzen on October 23.
Madrid again started the game less than fully focused, which was a feature of the ill-fated start to the season under previous coach Julen Lopetegui. I'm very happy but this was all about the players - we have some brilliant players here who have no limits. "We have seen lovely goals and I enjoyed them".
FW Karim Benzema, 8 - The often maligned Frenchman's opener tonight was highest quality, driving into the box and then dummying three Plzen players before expertly finishing for his 200th goal for Madrid. "I am only thinking of the next game". In football the most important is always the next game.
An unmarked Benzema notched his second goal in the 37th minute with a redirected header assisted by Gareth Bale to give Real a 3-0 lead and Benzema returned the favour minutes later when he flicked on a cross for Bale to sweep home a volley.
"We are facing up with Solari as coach of Madrid", Casemiro said.
"Julen is a great coach but we are with Solari now, and playing with more confidence", Benzema said.
What turned into a comfortable night for Real began in nervy fashion as Czech champions Plzen began brightly with Patrik Hrosovsky's cross cannoning off Nacho and hitting the woodwork.