The French outfit went ahead at Stadyen Dynama in Minsk after 14 minutes when Djibril Sidibe found the target from outside the box.
© AP Photos
Gorbunov failed to keep out the Lille forward on the half-hour mark as the Ligue 1 side doubled their advantage. Lucas Digne received a pass on the left side of the BATE penalty box, skipped past the challenge of Denis Polyakov and set up Bruno for a neat finish.
Four minutes from the half-time interval, it almost became 3-0 to Lille when Bruno failed to keep his shot from a Kalou cross on target.
There were fewer chances for either side in the second half, which saw Lille go down to 10 men after Sidibe was sent off for a second bookable offence.