The hosts made a strong start to the match and Miguel Britos almost gave them an early lead when his header was turned wide of the post.
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The visitors then wasted a huge opportunity to break the deadlock when Giulio Migliaccio's strike deflected kindly into the path of Alejandro Gomez, but from just a few yards out, the striker put his effort over the bar.
As the first half progressed Napoli enjoyed plenty of possession and Manolo Gabbiadini caused the Atalanta defence a moment of panic with a powerful free kick that was beaten to safety by Marco Sportiello.
However, the visitors withstood further pressure to go into the break on level terms.