Dzeko also scored in the stunning 4-2 win over the same opponents in Genk on Saturday, and this latest success kept Bosnia in second place in Group 5, six points behind leaders Spain.The Wolfsburg forward scored the first goal in the 12th minute following a corner, and struck again three minutes later after a pass from Senijad Ibricic.
Belgium were reduced to ten men just after the hour when Alex Witsel was sent off for violent conduct, but grabbed a consolation goal two minutes from time through Gill Swerts.
"We demostrated a heroic and tactical defence," said Bosnia coach Miroslav Blazevic.
Bosnians celebrated in the streets of the capital Sarajevo and other big towns, honking car horns and setting off fireworks.
Bosnia are bidding to reach their first major tournament as an independent nation.