Lorenzo Insigne checked Pierluigi Gollini in the opening minutes, while David Ospina had to fingertip a looping Muriel free-kick from the far top of the corner.
As Matteo Pessina ran through the ball into the inspired Muriel, denied by the legs of Ospina, Atalanta had a double chance, then the Remo Freuler rebound was blocked by Giovanni Di Lorenzo.
Rafael Toloi broke into the box after a give-and-go with Pessina, doing all right but the end, prodding wide away from the outside of the boot from 10 yards.
Atalanta continued to dominate the first half, Duvan Zapata shining a volley over at the back post and scuffing its finish at Ospina.
Finally, on the half-time stroke, Napoli had a chance, Diego Demme turning on a sixpence inside the field for a deflected angled drive just deep.
Within seconds of the restart, Atalanta struck again, Ospina racing off his line for a desperate interception, smothering at Muriel’s feet.
Ospina also blocked the Duvan Zapata header from a corner, while Cristian Romero was booked and is going to be suspended for the second leg.
Diego Demme had to be spread off after being accidentally fired in the chest by football from point-blank range on a Marten de Roon clearance, leaving dazed.
For long stretches, the visitors pinched Napoli back into their half again, but Toloi reached a corner with a fresh-air shot and Koulibaly deflected Muriel’s attempt.
Robin Gosens saw a big flash of his header from a Berat Djimsiti cross, as Kalidou Koulibaly nodded in a rare Napoli foray forward at a corner.