A superb solo strike provided Benzema's landmark moment and put Madrid on the path to a commanding win that sent them top of Group G in Santiago Solari's first European match at the helm.
The opener came after Sergio Ramos escaped punishment for an elbow on Milan Havel, but there was no stopping the visitors as Casemiro extended their lead in the 23rd minute.
Benzema doubled his tally and set up Gareth Bale in the space of 144 seconds towards the end of the first half, and Toni Kroos floated a beautiful 67th-minute chip home to wrap up the win and leave Plzen playing solely for third place.
Madrid's injury-hit defence almost conceded in the ninth minute when Nacho Fernandez sent Patrik Hrosovsky's cross against the bar.
Havel was left with a bloody nose after being caught by Ramos' in a 14th-minute challenge, and the injury sustained by the Plzen midfielder eventually led to his first-half withdrawal.
Madrid soon asserted its superiority when Benzema was granted space to run into and he used it to slot his milestone strike between the legs of Ales Hruska in the 20th minute.
More shoddy defending from Plzen enabled Casemiro to glance Kroos' corner home, before Benzema took his tally for Madrid to 201 by nodding Bale's cushioned header past Hruska.
The Frenchman returned the favour three minutes later, flicking Sergio Reguilon's delivery on for Bale to volley back across goal and into the bottom-left corner.
Solari handed Javi Sanchez and Vinicius Junior Champions League debuts in place of Ramos and Benzema and the Brazilian marked the occasion by setting up Kroos for a fine goal.
Lucas Vazquez was denied by a contentious offside decision and Bale rattled the upright in stoppage time as Madrid cantered to three important points.