Remi Garde's men came into the match with a 4-1 advantage from the first leg and the tie looked to be dead and buried when Bafetimbi Gomis fired them ahead on the night late in the first half.
But two quick-fire goals from Daniel Kolar and Stanislav Tecl gave the home side the lead and the latter had the chance to really apply the pressure from the penalty spot shortly after.
Tecl hit the post with his spot-kick, however, and it finished 2-1 on the night with Lyon moving through.
The Czech side had spoken before the game of the need for an early goal and a chance presented itself in just the third minute as Kolar scuffed wide from close range.
The home team were having the bulk of the possession and Tomas Horava and Milan Petrzela both had chances which missed the target but it was Lyon who came closest to breaking the deadlock.
Yoann Gourcuff swung a cross in from the right and Corentin Tolisso got on the end of it only to see his header come bouncing back off the post.
Plzen soon had a good chance of their own as Marian Cisovsky got on the end of a hopeful ball but his shot was brilliantly palmed away by Anthony Lopes.
Kolar then put a shot over the bar but any hope of an upset was effectively ended in first-half injury time as Gomis fired Lyon in front.
A ball from Milan Bisevac found the France international who cut into the box and unleashed a shot from 18 yards which went beyond Petr Bolek and into the far corner.
Bakary Kone headed wide just after the break as Lyon attempted to extend their lead before two goals in as many minutes offered the home side a glimmer of hope.
Kolar finally got the goal he had been pushing for all evening on the hour mark as he slotted home low from Patrik Hrosovsky's cross.
And just moments later Plzen were ahead on the night when Tecl headed home Petrzela's delivery from six yards.
The Czechs must then have thought the comeback was really on as, 19 minutes from time, Mouhamadou Dabo clipped the heels of Michal Durisin the penalty box.
Tecl stepped up to take the chance to reduce the aggregate deficit to just one but he hit the post after sending the goalkeeper the wrong way and the ball rebounded to safety.
Plzen continued to press in the closing stages but could not break Lyon down as the French side progressed to the last-eight.