Lille failed to make it out of the group stage in last season's Champions League and Rudi Garcia's team was eager to make a strong impression this time around.
But midfielder Aleksandr Volodko put the visitors ahead after just six minutes, striker Vitali Rodionov made it 2-0 in the 20th, and Edgar Olekhnovich added another just before the break to pile the pressure on Lille.
Center half Aurelien Chedjou pulled a goal back on the hour mark, but Lille failed to create enough chances to salvage even a draw against the Belarus side.
With Champions League runner-up Bayern Munich also in Group F, Lille faces a tough task to qualify.
Lille had a lot of possession but the visitors clinical attacking, led by former Arsenal midfielder Aleksandr Hleb, proved too much for Garcia's team to cope with.
Salomon Kalou returned from suspension to take his place on the right of Lille's attack, with Brazilian Tulio De Melo the lone center forward.
But Lille fell asleep in defense, allowing Volodko to turn in space and hit a shot from 20 yards (meters) that flew past goalkeeper Mickael Landreau and into the top right corner.
Mathieu Debuchy almost equalized for Lille moments later, but his low shot was pushed away for a corner by goalkeeper Andrei Gorbunov.
Rather than showing a patient approach, Lille poured forward in numbers and was soon caught out again.
Hleb started the move, threading the ball through to the midfielder Olekhnovich, who then gave Rodionov a simple tap-in from close range.
Lille midfielder Marvin Martin missed a good chance after Gorbunov came for a cross and missed the ball, leaving Martin with a chance that he wasted, firing the ball high over the crossbar.
Things got much worse for Lille when Olekhnovich rifled a shot in at the second attempt in the 43rd to leave Lille with an almost impossible task in the second half.
Garcia made changes, bringing on strikers Nolan Roux and Ryan Mendes, but it was Chedjou who gave the home side hope when he headed in Dimitri Payet's corner on the hour mark.
Roux went close with an audacious backheel that rolled just wide in the 79th, but Lille's attacks petered out as the visitors held firm.