Northern Ireland's Will Grigg scored in stoppage time but it proved a mere consolation.
The hosts had dominated early on but fell behind when Edin Dzeko's cross was flicked in by Duljevic in the 36th minute.
A defensive mix-up between defender Craig Cathcart and goalkeeper Bailey Peacock-Farrell allowed Saric to double the lead in the 64th minute.
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Northern Ireland were guilty of several wasted opportunities as they made a poor start to a new competition that could offer a secondary route to the Euro 2020 championship.
Austria are the other team in Group B3 with the teams playing each other home and away.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
