The Belarus outfit looked a shadow of the side which beat Bayern Munich 3-1 on home turf earlier in the tournament as Rudi Garcia's youthful charges ran out comfortable winners
Two first-half strikes from Djibril Sidibe and Champions League debutant Gianni Bruno were enough to earn Rudi Garcia's charges a comfortable victory over their Belarusian hosts, who offered little to nothing by way of attack throughout the match despite having beaten Bayern Munich earlier in the tournament with an impressive display.
The result gave les Dogues their first points of their European campaign this season, and almost certainly consigned the Belarusian champions to the Europa League for the remainder of the season before Bayern and Valencia had even kicked off their match.
The hosts enjoyed the lion's share of the possession early on, but it was the Ligue 1 side who struck the first blow in the first quarter of an hour. Some clever link-up play between Bruno and Salomon Kalou eventually saw the ball break for Djibril Sidibe, who curled a delightful effort beyond the fingertips of Andrey Gorbunov and into the far corner.
BATE were stunned after conrolling the opening, and had a chance to hit back straight away when Vitali Rodionov latched on to a loose ball on the Lille area, but he could only fire over the bar from close range.
The play began to stretch as both sides looked to score the important second of the night. Bruno had a chance to open his account amongst Europe's elite when Gorbunov's clearance fell straight to him, but he failed to keep his effort down. At the other end, Renan Bressan slipped in behind the Lille line and clipped the ball back across but failed to find any waiting team-mates, before the no.10 shot wide when set up by Aliaksandr Hleb moments later.
BATE were struggling to keep a rhythm to their attacking play and, shortly before the break, Lille doubled their advantage with a well-worked counter attack. Lucas Digne strode down the left flank and skipped effortlessly past the static Polyakov before cutting back for Bruno, who tapped home from point-blank range to notch a debut Champions League goal.
Lille were playing with a confidence which belied their pointless campaign so far this season, and the lively Kalou almost set up a third after tricking his way past Artem Radkov before setting up Bruno, who this time could only fire over the bar from close range.
Artyom Kontsevoi came on at the break to add life to the hosts' lackluste attack, and he set up a chance for Bressan when robbed Digne and crossed into the middle, but Elana was off his line smartly to smother the danger.
Lille came close to a third shortly before the hour mark when Polyakov cleared Marvin Martin's effort off the line after Gorbunov had raced off his line to deny Kalou a clear run at goal, before Martin again threatened the fragile BATE back line with a teasing cross which just eluded his attackers.
BATE knew they were in with a strong shout of progressing to the knock-out phase before the game, but their lackluste attacking display was in stark contrast to their earlier impressive performances. Bressan flighted in a number of set-pieces to little avail, with Rozehnal's frantic clearanc following a goal-mouth scramble the only real time les Dogues were troubled by his delivery.
However, they were handed a lifeline when Sidibe was dismissed for a late trip on Maksim Bordachov, with the referee strangely issuing a straight red even though the defender had already been booked and perhaps deserved to pick up nothing more than a second yellow.
BATE packed the attack in response and forced Elana into a save following a scramble in the penalty area, but they failed to pick up the tempo sufficiently and Lille looked no more troubled with ten men than they had with nine, leaving the hosts to rue a missed opportunity and prepare for a campaign in the Europa League after the winter break.