Arsenal produced the worst display since Unai Emery's appointment against BATE Borisov in the Europa League, according to former defender Martin Keown.
Stanislav Dragun's first-half header was enough to ensure the Belarusian champions will take a one-goal advantage into the second leg at the Emirates Stadium next week.
Alexandre Lacazette compounded a hopeless evening by being sent-off late on for an elbow on Aleksandar Filipovic to end any hope of a comeback.
Editors' Picks
Defeat was the fourth in the last seven games in all competitions for Emery, whose encouraging start is quickly being replaced by a typical mid-season downturn.