Djuric, who stands 1.99 metres tall, scored the first and set up the second in Saturday's 2-0 home win over Wales, then grabbed the winner in Tuesday's 3-2 victory in Cyprus which allowed the Bosnians to finish third in Group B.
Djuric, who was making just his fourth international appearance, deflected the focus onto team mate Haris Medunjanin, who netted Bosnia's first two goals against the Cypriots.
"I congratulate Haris, he's had a tough time but he scored two goals and showed what kind of a player he is," Djuric told Bosnian media after the win in Nicosia.
"We are overjoyed. It wasn't easy because Cyprus played very well but we're off to the playoffs now. I hope we can finish the job when we return in a month's time."
Like Deportivo La Coruna midfielder Medunjanin, Djuric has fallen down the pecking order at his club this season, struggling to make an impact at Italian second division side Cesena.
The draw for the playoffs, which also feature Norway, Sweden, Denmark, Ireland, Slovenia, Ukraine and Hungary, will be held in Nyon on Sunday.
The Bosnians will face a two-legged tie to be played between Nov. 12 and 17, with the winners clinching the last four remaining berths for next year's tournament in France.
It will be Bosnia's third involvement in the playoffs of a major tournament after they were knocked out by Portugal in the final qualifying stages for the 2010 World Cup and Euro 2012.
They were knocked out in the group stage of the 2014 World Cup, their maiden appearance on the big stage as an independent nation.
Coach Mehmed Bazdarevic said there was no easy draw.
"It will be tough in the playoffs no matter who we are pitted against, but this team has a huge potential and I believe we can beat much stronger teams than the last two we defeated," he said.
"Dzeko was not 100 percent fit for the run-in and I went with Djuric, which turned out to be the right decision.
"We won both matches and also spared Dzeko, who can now recover in peace for the November playoffs."
(Writing by Zoran Milosavljevic in Belgrade; Editing by Peter Rutherford)
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