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The Giallorossi made it four points from a possible six after a hard night's work at the Olympic Stadium in Baku, with Dzeko scoring what would turn out to be the winner - after Kostas Manolas had opened the scoring.
Pedro Henrique halved the deficit to set up an anxious second half, but Eusebio Di Francesco's side eventually held on.
"It was important to win tonight, perhaps more than it was to play well," Dzeko said. "We should have put the game to bed in the first half, but everything was harder after they scored.
"We dug in together – that’s the way it should be – and at the end of the day we got the three points."
Dzeko pinpointed Qarabag's goal as a turning point in the contest, giving both the team and the near-70,000 fans in attendance a huge boost.
"Yeah, we started really well and got two goals early, but then we conceded and that boosted Qarabag’s confidence," he added. "They pressed us high up the field and we weren’t able to play our game. It wasn’t an easy game to win tonight, but we did win and in the end the most important thing is the three points.
"The big teams get through the tough periods together and that’s a good quality to have. It wasn’t easy today, even though everybody thought it was going to be. Perhaps we thought that a bit too."
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