Trailing 4-1 from the first leg against a side previously unbeaten in the competition this season, Plzen looked dead and buried on Thursday when Bafetimbi Gomis scored his 19th goal of the season in first-half stoppage time.
Daniel Kolar and Stanislav Tecl netted within two minutes of each other around the hour mark to give Plzen hope, but the latter then fluffed his lines when presented with a glorious chance to cut the overall deficit to one goal as his penalty struck a post.
That came as a fatal blow to Plzen's hopes of a remarkable comeback, but they did inflict a first European defeat on their Ligue 1 visitors in 10 matches this season.
Remi Garde's side were without last week's two-goal hero Gueida Fofana through injury, and were almost behind early on but Kolar scuffed wide from six yards.
The Czech champions knew an early goal was necessary if they were to claw back the three-goal deficit and nearly got the breakthrough when Tomas Horava's 25-yard effort took a deflection before squirming just wide with Anthony Lopes struggling.
Gomis saw his shot from a narrow angle blocked but Lyon's attacks were rare and it was Plzen who again threatened through Milan Petrzela, the midfielder controlling a high ball brilliantly before lashing over from close range.
For all Plzen's efforts, Lyon carved out the best chance of the half after 27 minutes. Yoann Gourcuff's superb free-kick was headed against the post by Corentin Tolisso and the rebound fell to Jimmy Briand, who somehow missed the target with the goal at his mercy.
Anthony Lopes then produced a stunning save to keep the second-leg scores level, somehow keeping out Marian Cisovsky's close-range volley.
And that proved pivotal as Lyon seemingly put the tie beyond the hosts' reach in first-half stoppage time, Gomis cutting in from the right before steering a low shot into the bottom-left corner with precision.
To their credit, Plzen fought on and Anthony Lopes saved superbly again from Cisovsky before the Czechs turned the match on its head.
First, Kolar latched on to Patrik Hrosovsky's pass to emphatically rifle home, and after 62 minutes Tecl was on hand to direct a header in off the post from close range.
They had the chance to put serious pressure on the visitors 20 minutes from time when Mouhamadou Dabo tripped Michal Duris in the box, but Tecl's penalty cannoned back off the woodwork and Lyon held on to reach the last eight.
