Glabdach, who conceded late equalisers in their previous group matches against Inter Milan and Real Madrid, scored four in the first half, with two coming from the 27-year-old Plea, to kill off the game and eventually earn one of the largest away wins of the competition.
They are now top of Group B on five points from three games, one point ahead of Shakhtar.
Gladbach, now on an eight-game unbeaten run in all competitions, caught Shakhtar by surprise with a two-pass counter attack and Stefan Lainer finding space down the right to cut back for Frenchman Plea, who scored with a crisp finish in the eighth minute.
A Plea missile from 25 metres put the game beyond the hosts before Ramy Bensebaini added a fourth a minute before the break.