Los Blancos entered the match having lost four of their last five in all competitions, but a goal in either half proved enough for the European champions, who have moved to the top of Group G on six points, to triumph despite the visitors registering late on.
Sergio Ramos had the game's first half-chance in the fourth minute, but his header sailed over the Plzen crossbar.
The visitors had a super chance of their own in the 11th minute when Milan Petrzela found space inside the Real Madrid box, but Keylor Navas - in for Thibaut Courtois - was on hand to make a fine save, before the Plzen attacker sent his second attempt wide of the post.
Los Blancos had more than 70% of the possession in the first 25 minutes, but the hosts were far from at full flow, and Plzen should have levelled on the 30-minute mark when David Limbersky broke into the box, but the number eight sent his effort just wide.
Plzen goalkeeper Ales Hruska then had to keep out a close-range attempt from Benzema as chances arrived at both ends.
Real Madrid did have the ball in the back of the Plzen net for a second time in the 33rd minute when Gareth Bale swept into the corner, but the Welshman was rightly called offside.
Isco was next to come close for the home side following a mistake in the Plzen defence, with the Spaniard's chipped effort just dropping wide of the far post, before Hruska made a super save to deny the 26-year-old from a short corner.
The away side had a huge chance to level the scores early in the second half when Michael Krmencik found Havel with an excellent cross, but the attacker sent his volley wide of the post.
Bale then struck over the crossbar down the other end as both teams had opportunities to add to the scoring.
Real Madrid had their second in the 56th minute, with Marcelo meeting a cute pass from Bale before expertly chipping the ball over the onrushing Hruska to settle the nerves inside the stadium.
Bale headed over the Plzen crossbar 10 minutes later as the home side searched for a second, before the Welshman struck over the crossbar from distance as the score stayed 2-0.
Benzema put the ball in the back of the Plzen net in the 71st minute, but the Frenchman was ruled offside.
Plzen had one back in the 79th minute when Hrosovsky collected a pass from Ales Cermak before finding the back of the net with a fine finish, and it was no more than the Czech outfit deserved.
The home supporters were noticeably nervous approaching the final stages of the affair, but Real Madrid closed it out to secure three important points ahead of El Clasico this weekend.
REAL MADRID (4-3-3): Navas; Lucas, Ramos, Nacho, Marcelo; Modric, Kroos, Casemiro; Bale (Asensio 75'), Benzema (Mariano 88'), Isco (Valverde 54')
VIKTORIA PLZEN (4-2-3-1): Hruska; Reznik, Hejda, Hubnik, Limbersky; Hrosovsky, Prochazka (Horava 65'); Havel (Ekpai 76'), Cermak, Petrzela (Reznicek 86'); Krmencik