Scamacca drove home his 10th goal of the season in all competitions on the stroke of half-time after pinching the ball from a dozing Jesus and exchanging passes with Miranchuk.
Napoli were loudly booed off when the teams left the field shortly afterwards and the hosts responded to that displeasure after the break.
The hosts were unlucky not to pull a goal back when Piotr Zielinski and Victor Osimhen both hit the woodwork in the 55th minute.
And Osimhen was twice denied by Atalanta keeper Marco Carnesecchi before Koopmeiners made absolutely sure of the points with a precision left-footed finish to provoke another loud round of dissent from the stands.