The win put BATE six points clear of second-placed Shakhtyor Soligorsk, who crushed Neman Grodno 4-0 earlier on Sunday.
BATE are assured of finishing first because they have more wins than their rivals.
Brazil-born midfielder Renan Bressan and Belarus international Vitaly Rodionov each scored twice to lead BATE to their 20th victory in 28 league matches.
BATE captured their ninth national championship since 1992 and they now have two more titles than Dynamo Minsk, who also won the Soviet championship in 1982.
BATE, a modest club with limited resources, have also made headlines in Europe this season, beating Germany's Bayern Munich and France's Lille in the Champions League.