The Europa League holders were frustrated throughout in Madrid, though only a last-gasp winner spared their blushes as they maintained their record in this competition
The holders failed to seriously trouble the visitors, who showed defensive grit and determination, and should have at least gained a point for their efforts, had it not been for a 92nd minute winner from Cristian Rodriguez.
Diego Simeone rang the changes from the side that beat Espanyol on Sunday, with as many as nine new faces coming in, including the likes of Cisma, Jorge Pulido and Abdelkader Oueslati as the holders aimed to continue their dazzling run in this competition.
The first 45 minutes proved to be a very mundane affair, with the Czech side happy to restrict Atletico to possession in their own half. The first real chance of note was spurned by Emre, whose fierce effort outside the area narrowly zipped past the post.
Sergio Asenjo had pretty much nothing to contend with for much of the period, except for an almost embarrassing moment where the ball slipped from his grasp and was nearly turned in by Vaclav Prochazka, with the referee instead, awarding a free-kick in the goalkeeper's favour.
Towards the end of the half, the play was stepped up. Frantisek Rajtoral sped past his marker on the right wing, delivering a superb cross in towards Marek Bakos, who nudged his header wide of Asenjo's left post, before Koke's measured attempt proved to be an easy take for Matus Kozacik.
Pavel Vrba's men should have easily taken the lead just before half-time, when Emre was criminally caught in possession by Marek Hanousik in his own area, though the hosts were spared, after the midfielder's cut-back was hurriedly cleared by Pulido.
The second period fared no better, as Atleti failed to negotiate past a compact and resolute Plzen defence, with the best chance falling to the visitors, as Prochazka fired a curling free-kick which had Asenjo at full stretch to parry away.
Raul Garcia and Tiago came off the bench on the hour, replacing Diego Costa and Koke to add further impetus to Atletico's struggling attacking players. Cristian Rodriguez was then felled by Renzik in the box, though referee Anthony Gautier immediately waved play on, much to the annoyance of the player.
Simeone's inexperienced side were again dealt with easily by the visitors, though Emre almost forced through an opening, with his slightly miscued chip shot ending up in the hands of the goalkeeper.
With time petering out, Raul Garcia almost made it a smash-and-grab victory, though his close-range header in injury time was to be parried away by Kozacik before Cristian Rodriguez's late intervention saw him produce a fine finish to lash home from 20 yards and steal victory at the death.