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 their 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.
What does it mean? Roma trip could define top spot
With Madrid and Roma locked on nine points at the top of the group, their clash at the Stadio Olimpico in three weeks could well prove pivotal to who potentially earns a better draw in the last 16. If Solari can continue his winning start into that match, it will be tough to see past Madrid getting what they need to finish top.
Benzema back on song
By surpassing 200 goals for Madrid, Benzema became just the seventh player to reach the total in the club's history, joining names like Cristiano Ronaldo, Raul and Alfredo Di Stefano. Having struggled so much in front of goal over the past two months, he now has four in his last five outings in all competitions and will hope to maintain his resurgent form.
Limbersky at a loss
Plzen left-back David Limbersky appeared to duck out of the way when Casemiro rose to head in Madrid's second, and his lack of aerial prowess was exploited again by Bale and Benzema as they assisted one another to take the visitors' tally to four before half-time.
10 - Gareth Bale has been directly involved in 10 goals in his last eight Champions League group stage games for Real Madrid (five goals, five assists). Impact. pic.twitter.com/a4bTPFspLh— OptaJoe (@OptaJoe) November 7, 2018
Key Opta Facts
- Santigo Solari is the second Real Madrid manager to win his first three competitive games without conceding a goal (Luis Carniglia in 1957).
- This 5-0 victory is the biggest win by a Spanish side away from home against a Czech team in European competition.
- Real Madrid's Karim Benzema has scored more headed goals than any other LaLiga player this season in all competitions (four).
- Toni Kroos provided his 50th assist for Real Madrid in all competitions and his first this season for the club.
- Madrid's Gareth Bale has been involved in 10 goals in his last eight Champions League group stage games (five goals, five assists).
- Czech and Spanish clubs have met 10 times previously in the Champions League – Spanish clubs have won all of those 10 games, scoring at least twice in each victory.
Madrid will be hoping to close in on LaLiga's top four when they travel to Balaidos to face Celta Vigo on Sunday, while Plzen take on Pribram at home on the same day.