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.
Inter and Real, on two and one point respectively from two games, play each other later on Tuesday.
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 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.
Lars Stindl made the most of a Trubin error to put his team 5-0 ahead in the 65th, before Plea beat the offside trap to complete his hat trick with a fine finish.