Tomas Horava put the visitors into the lead after just three minutes, but Gueida Fofana's double - either side of Alexandre Lacazette and Arnold Mvuemba's strikes - sealed the win
Plzen drew first blood at the Stade de Gerland after just three minutes through Tomas Horava's low header, but Lyon soon hit back as Gueida Fofana's knee diverted a corner kick past Petr Bolek.
Stanislav Tecl shot wide late in the first half and was made to pay for his miss as Lyon overwhelmed Plzen after the restart.
Alexandre Lacazette drove home Steed Malbranque's inviting through-ball before the veteran midfielder set up Arnold Mvuemba to give Lyon breathing space.
And Fofana popped up after 69 minutes to make the game safe and leave Plzen facing a huge task to reach the quarter-finals when the sides clash again in the second leg next week.
The result stretches Lyon's impressive Europa League record to one defeat in their last 17 games, but they had to dig deep.
The Czech champions enjoyed a great start and took the lead after three minutes when Jan Kovarik's left-wing cross was perfect for Horava to nod past Anthony Lopes.
Remi Garde's Lyon, though, responded well and were back on level terms after 12 minutes when Malbranque's corner was directed in off the knee of Fofana.
Tecl weaved through the home defence and fired a low effort that was easily dealt with by Anthony Lopes as Plzen went in search of a second.
Lacazette flashed a volley wide of Bolek's near post as the game flowed from end to end before Fofana saw his speculative effort saved after 25 minutes.
Bolek had to be alert again when Mvuemba's swerving free kick bounced in front of him but he clawed it away.
Despite being on the back foot, Plzen ought to have regained the lead when Tecl robbed Milan Bisevac, but failed to hit the target.
And the visitors went closer a minute before half-time through David Limbersky's rasping effort that Anthony Lopes did well to tip behind.
Plzen were punished for missed chances early in the second half when Malbranque stole the ball in midfield and, after exchanging passes, slipped the ball to Lacazette, who drove home convincingly.
That goal gave Lyon the opportunity to defend deep and hit on the break, which they did to devastating effect on the hour mark.
Malbranque was again influential, lifting an inch-perfect ball to the onrushing Mvuemba and controlled superbly with his chest before lashing home emphatically.
And Lyon made it four after 69 minutes when Fofana ran on to Lacazette's ball to slam home via a deflection on the edge of the area.