The result keeps the Champions League winners in each of the last three seasons on course to make the last-16 of this year's competition, while Solari is now the first Madrid manager since the 1950s to win each of his first three games in charge, while keeping three clean sheets.
The 42-year-old Argentinian dismissed questions about his possible future as Real's head coach. "I am only thinking of the next game".
Pressed as to whether he now saw himself likely to get the job permanently, Solari said he could only think about Saturday's La Liga game at Celta Vigo.
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 attractive 67th-minute chip home to wrap up the win and leave Plzen playing exclusively for third place.
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. "We live in permanent crisis all the time, even when we are winning the Champions League".
Kroos rounded off the scoring in the 68th minute, curling a sumptuous lob over the stranded Hruska following a pass from rising star Vinicius Junior, who came on as a second-half substitute.
With two games remaining in Group G reigning champions Real are joint top on nine points with AS Roma who beat CSKA Moscow 2-1.
That lone goal was against, you guessed it, Viktoria Plzen two weeks ago.
Real overcame an early scare when Nacho cleared a low cross against his own crossbar, while Plzen midfielder Roman Prochazka curled a shot just past Thibaut Courtois's goal.
Benzema then narrowly missed Bale's cross just in front of a gaping goal. "The man who asks that doesn't know Madrid, no?"
Lucas Vazquez was denied by a contentious offside decision and Bale rattled the upright in stoppage time as Madrid cantered to three important points.