The victory kept the home side's hopes of qualification alive as they lie third in the table behind leaders England, 4-0 winners earlier in Kazakhstan, and second-placed Croatia.
It was a sixth loss in as many qualifying games for Andorra. With a trip to England to face the group leaders at Wembley on Wednesday next up, things do not get any easier for the minnows.
Bliznyuk opened the scoring after two minutes and added his second after 76 minutes to put the home side 5-0 up. Timofey Kalachev had put Belarus 2-0 up just before half-time and two goals from Kornilenko put the result beyond doubt.
Ildefons Lima scored a consolation for the visitors from the penalty spot four minutes into injury time.