Manchester City striker Edin Dzeko scored twice and Zvjezdan Misimovic and Vedad Ibisevic added the other two goals in a frantic spell between the 27th and 39th minutes to keep Bosnia top of the group before Tuesday's final round of matches.
Nicolas Hasler pulled one back for the visitors in the 61st minute.
The win lifted Bosnia to 22 points from nine games, three more than Greece who faced Slovakia at home later on Friday.
Bosnia, who were treated to a standing ovation by their noisy fans after the final whistle, enjoy a vastly superior goal difference to Greece so if they win in Lithuania on Tuesday a place in Brazil will almost certainly be secured.
(Writing by Zoran Milosavljevic, Editing by Tom Bartlett and Sonia Oxley)
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