Dzeko's side battled to a 0-0 draw with Austria in Vienna, ensuring they could not be overtaken at the top of their group and guaranteeing their place in the top tier of the next edition of the competition.
Afterwards Dzeko, who played all 90 minutes, took to social media to thank the fans for their support.
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"Thank you for the incredible support from the stands tonight," Dzeko wrote.
"With your power behind us, we felt like we were playing it home. Now you should celebrate this, because we all deserve to enjoy it together."
Elsewhere, Patrik Schick played 77 minutes in attack, as the Czech Republic secured a 1-0 away victory against Poland in a friendly. Sampdoria's Jakub Jankto scored the only goal of the game for the visitors.
Defender Kostas Manolas was also in action on Thursday - but was withdrawn early on with an injury, as Greece ended up 1-0 winners over Finland, although it was not enough to keep their Nations League hopes alive.
Finally, midfielder Nicolo Zaniolo was in Under-21 action - starting for the Azzurri in their eventual 2-1 home defeat against England U21s.
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