A 1-0 win for Serbia over Hungary earlier in the evening meant the best Finland could do was win to stay three points behind group leaders Serbia and ensure they would finish no lower than second in the group.
After playing their first home matches in Italy and Serbia, respectively, Hungary was the location for Belarus' final home match in the group, with the Szent Gellert Forum in Szeged playing host.
The lack of home comforts certainly did not help the Belarusians, who found themselves behind after eight minutes when Sanni Franssi opened the scoring for Finland.
The Boreal Owls were struggling to seal the points against a side who were fighting to drag themselves off the bottom of the standings, but they finally killed off the tie after the hour mark thanks to an experienced head.
On the occasion of her 150th cap, 36-year-old striker Sallstrom scored twice in a seven-minute spell - her 63rd and 64th international goals - to settle the tie in Marko Saloranta's side's favour.
The 3-0 win sees Finland move onto 10 points, seven clear of Hungary, while Belarus stay bottom on two.
On Tuesday, Finland welcome Serbia to Helsinki's Olympic Stadium knowing a win will secure promotion to League A, while a draw or a defeat will see them head into the promotion playoffs.