The game in Zenica ended 1-1 after extra time, with Bosnia coming from behind against 10-man Italy in a match full of dramatic twists and turns, and Dzeko hit the deck in the dying seconds after a foul by Davide Frattesi.
Home fans must have feared the worst when Bosnia's all-time top scorer made his way to the centre circle for the coin toss holding an ice pack on his shoulder, and in the end, the striker left the pre-shootout formalities to a teammate.
"I keep saying it must have been fate, for it to happen in the last second of the match, and then for me not to be able to take a penalty," Dzeko said at a euphoric press conference on Wednesday.
"Someone else stepped up instead of me, scored, and in the end, we won.
"Who knows, maybe if I had taken it, I wouldn't have scored, so it all feels like it comes from above."
Bosnian keeper Nikola Vasilj did not even need to make a save during the shootout. Pio Esposito blazed Italy's first spot kick high over the bar and Bryan Cristante's penalty rocked the crossbar, while the hosts put away all four penalties.
Bosnia's final two takers, 18‑year‑old Kerim Alajbegovic and 21‑year‑old Esmir Bajraktarevic, have a combined age lower than Dzeko's, yet both stepped up with remarkable composure to convert.
Dzeko, who played and scored in Bosnia's only previous World Cup appearance in 2014, joined in the jubilant celebrations wearing a sling - still in place during the press conference - but sounded optimistic about his prospects of recovering in time for the finals.
"We're all relieved about the arm, it's not the worst‑case scenario," Dzeko said.
"Most likely it won't need surgery. So I hope that in maybe a month, month and a half, I should be back."