The result left the Greeks second in the group on 12 points from six games, four behind leaders Belgium and one ahead of the third-placed Bosnians.
Europe's nine group winners will qualify automatically for next year's 32-team tournament in Russia while the eight best runners-up will enter a two-legged playoff for the remaining four places.
Having jeered the Greek national anthem before kick-off, Bosnian fans were given little to cheer about by a toothless home side whose adventurous 4-2-3-1 formation failed to create many clear-cut chances.
Deploying striker Vedad Ibisevic in a deeper role behind lone hitman Edin Dzeko backfired for the home team's coach Mehmed Bazdarevic, whose side struggled against a packed and well organised Greek rearguard.
On the rare occasions when the home team managed to put neat passes together in the first half, Greek goalkeeper Orestis Karnezis stepped up to deny Edin Visca and substitute Kenan Kodro in a contest littered with fouls.
Forward Kodro replaced Senad Lulic in the early stages after the left back came off with a head injury but made way for midfielder Muhamed Besic in the 75th minute after looking completely at sea in an unfamiliar position.
The ultra-defensive Greeks missed the game's best chance in the 82nd minute after they broke down the left flank, only for right winger Petros Mantalos to fire over the bar from 10 metres with the goal at his mercy.
Dzeko and centre back Toni Sunjic forced two good saves from Karnezis as the visitors were forced to defend desperately in the closing stages.
(Writing by Zoran Milosavljevic in Belgrade; Editing by Ed Osmond)
