Stanislav Tecl's 11th goal of the season after 62 minutes looked set to give the Czechs the edge in this last-32 tie, but Luiz Adriano equalised to give Shakhtar an away goal.
Both sides were playing their first competitive match since the last round of the Champions League group stage back in December, but neither looked rusty.
Plzen were comfortable in possession, while Shakhtar were happy to soak up pressure and counter-attack at pace, with Alex Teixeira, Ismaily and Taison all coming close after swift attacks.
Shakhtar attacking power caused Plzen goalkeeper Matus Kozacik a couple of uncomfortable moments early on.
After Yaroslav Rakitskiy's speculative shot from a 35-yard free-kick went straight at Kozacik, but he still fumbled it.
And moments later Teixeira should have opened the scoring when he curled a shot just past a post with Kozacik stranded off his line.
It was Plzen's captain Pavel Horvath who had his side's best chance in the first half.
He attempted an audacious chip from 45 yards that the quickly retreating Shakhtar keeper Andrei Pyatov was relieved to see land on the roof of the net.
It was not until the 62nd minute that the first goal arrived.
A brilliant cushioned header down by Marian Cisovsky allowed Tecl to poke the ball home from six yards and give the hosts the lead.
But just four minutes later the 2009 UEFA Cup winners were level.
Luiz Adriano made a beautifully timed run in behind the Plzen defence and, after taking a wonderful first touch, placed the ball past Kozacik for his 15th goal of the season.
Teixeira and Luiz Adriano both had good chances to win the game for Mircea Lucescu's side, but neither could convert them.