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The striker scored twice, either side of half-time, to give his side the early advantage - before Kalidou Koulibaly's header set up a tense last half-hour. But Mohamed Salah slotted home in the closing stages to secure the three points, giving Roma an early advantage over their rivals at the top of Serie A.
"It's a massive win for us and a deserved one too," Dzeko said. "We managed to come here and play our game and that's never easy at Napoli's place.
"We scored three goals and we're really happy."
On his own form, which now sees him top of the Serie A goalscoring standings with seven goals, he said: "I'm feeling good and people believe in me. I'm pleased for myself but especially for the team because we've won a difficult game.
"You expect criticism because I didn't have a great season last year. I was determined to do better this season and that's what I'm doing."
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