The Ukrainian side had by far the better of the play but were unable to beat the hosts' goalkeeper and had to settle for the slight advantage of an away goal.
The Brazilian trio continued their threat throughout the half, with Costa in particular able to get behind the home defence several times.
Matus Kozacik remained strong in the Plzen goal though, punching, catching and blocking anything that came into the six-yard box to keep his side level at the break.
Shortly into the second half, almost out of nowhere, Stanislav Tecl found space inside the box and put the home side ahead.
Shakhtar continued to push forward in search of a winner but unfortunately were unable to really test the goalkeeper from then on in, and will be disappointed not to have gained a bigger advantage ahead of the second leg.