Revered in his home country and known as the Bosnian Diamond, there was a murmur of excitement from the crowd every time the City striker got hold of the ball in the opening stages.
He didn’t disappoint, grabbing a brace to take his international tally to a magnificent 28 goals in 52 games for his country.
It had been a tight game until Dzeko opened the scoring after half an hour, sending a powerful downward header to nestle in the corner of the net from a Zvjezdan Misimovic cross.
The home side took control after that and the City man put the gloss on what was a comprehensive victory with his side’s third - combining with Misimovic again to score another header past Karnezis in the Greece goal.
That leaves the Dragons in an excellent position to qualify for the 2014 World Cup in Brazil, as they sit top of Group G on 13 points.
Elsewhere, Matija Nastasic and Aleks Kolarov both played 90 minutes as a young Serbia side lost 2-0 to Croatia in Zagreb.
Always destined to be a fractious fixture, this was the first time the two sides have met since becoming independent nations.
The bloody history of conflict between them meant for a hostile atmosphere for the Serbian stars, and away fans were forbidden to travel to the stadium.
It was therefore encouraging to see Nastasic put in a relatively calm performance in difficult circumstances, and his budding partnership with Subotic will surely give Serbia hope for the future.
By contrast, Kolarov had a first half to forget as he played a part in both Croatia’s goals. His free kick in the Serbia half was charged down by Olic who squared for Mandzukic to slide the ball into the net.
He also conceded the free kick from which the home side scored their second. He was booked for the tackle, which means he will miss Tuesday’s home fixture with Scotland.
The defender returned reinvigorated after the break and drove forward to produce Serbia’s first decent chance of the match. He forced a very good save from Pletikosa in the Croatia goal after a good run down the left.
Brazil now looks a long way off for Serbia – they lie nine points behind the top two in Group A.
Costel Pantilimon was an unused substitute as Romania drew 2-2 away to Hungary.