Charles De Ketelaere returned to the starting XI for the first time since his impressive World Cup campaign for Belgium.
Giorgio Scalvini was unlucky not to break the deadlock after eight minutes, as his effort thumped the frame of the goal.
It was only a warning, as Scamacca finished off the assist from new signing Gianluca Gaetano.
Schalke 04 tested Marco Carnesecchi, and rattled the woodwork themselves with Karaman, before Samardzic struck on the counter-attack.
Carnesecchi was again decisive on Adamu, but Krstovic’s lovely bit of footwork to get away from Katic saw Atalanta run out 3-0 winners.
Elsewhere, Sassuolo visited Germany for their final re-season match and fought in a 3-2 thriller with Augsburg.
Andrea Pinamonti converted an early penalty earned by Josh Doig, while Cristian Volpato scored a great solo goal when sprinting forward and dribbling around the goalkeeper.
However, Augsburg turned the game around completely, with Fellhauer and Kade confirming the evident problems goalkeeper Arijanet Muric has dealing with crosses.
Behrens completely the comeback for the 3-2 German win.
Schalke 0-3 Atalanta
Scamacca 30 (A), Samardzic 39 (A), Krstovic 87 (A)
Atalanta: Carnesecchi; Bellanova (Zappacosta 46), Kossounou (I Sulemana 61), Scalvini, Ahanor (Bernasconi 46); Ederson (Kolasinac 61), Gaetano (De Roon 61), Samardzic (Pasalic 46); De Ketelaere (K Sulemana 46), Raspadori (Cassa 70); Scamacca (Krstovic 46)