The Czechs failed to hit their stride and Pierre Webo's late strike was deserved punishment for the home side's lack of attacking intent.
Fenerbahce went into the game on the back of two straight losses against Trabzonspor in the Turkish Cup and then Besiktas in the Super Lig, a defeat which saw them drop to third.
Aykut Kocaman's side were also without suspended duo Egemen Korkmaz and Raul Meireles.
Plzen's 5-0 aggregate thrashing of Napoli in the last round, coupled with their domestic form which has taken them to the top of the Czech League, made them big favourites against the Turkish side.
However it was Fenerbahce who started stronger, with Mehmet Topal's effort forcing a save by Matus Kozacik after 16 minutes.
Marek Bakos had the home side's first effort on goal after 25 minutes, but his header failed to land on target, before Volkan Demirel's first action came after a minute later after he cut out Pavel Horvath's cross.
Cristian Baroni failed to test Kozacik from 25 yards, before Topal was the next Fenerbahce player to miss the target from range.
The Turkish side continued to dominate possession and Kozacik did well to parry Baroni's effort.
This seemed to wake the Czechs and eight minutes before the interval came closest to breaking the deadlock.
Frantisek Rajtoral's left-footed effort from 18 yards crashed against the bar before Michal Duris' effort was blocked by Reto Ziegler.
After the break, it was Fenerbahce who were once again on the attack with Moussa Sow testing Kozacik after 58 minutes
Plzen striker Bakos was replaced by Stanislav Tecl on the hour mark and 10 minutes later Martin Fillo came on for Duris, but after their goal-fest against Napoli, their forwards were now feeding off scraps.
And it was little surprise when it was the visitors who broke the deadlock after 81 minutes.
Gokhan Gonul's cross from the right found Sow at the back post, and though Webo's header was well saved the Cameroonian followed in to put his side into the driving seat in the tie.