The victory also marked Real's third in a row in all competitions under their temporary coach, who said he was focused on the next game rather than his status at the club.
Things started to look more positive as his side then went on a six-match unbeaten run, including a 3-0 win over Roma in the Champions League and four further victories in La Liga.
It was a landmark night for Benzema, whose first goal was his 200th for the club.
Casemiro guided a simple second into the corner of the net after being left totally unmarked from a corner, before Benzema helped himself to another in nearly identical circumstances, this time once picked out by Gareth Bale's headed pass four yards out.
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Madrid were dominate throughout and Toni Kroos added an impressive fifth after the interval when he chipped goalkeeper from inside the area.
Benzema, who has made 429 appearances for the club in all competitions, is the seventh player to score at least 200 times for Madrid.
'Solari was also a Real Madrid player and he knows a lot about the game.
But any hopes Plzen harboured of a shock win were wiped out with two quickfire goals in the 21st and 23rd minutes. Find out by following our live matchcast.
Madrid beat Plzen 2-1 at home last month 2-1 with Julen Lopetegui at the helm before the former coach was sacked three months into his first season in charge after Real were thrashed by arch-rivals Barcelona. The Czech team tied CSKA Moscow on September 19, but then suffered a blowout loss to Roma on October 2, falling 5-0, before defeat at the Bernabeu.