Zaza would not have to wait too much longer for another chance, however, and this time he took full advantage, firing a deflected effort past the keeper for his first international goal.
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King came close again just before the half-hour mark as he worked space to shoot from outside the box, but his effort deflected just wide.
Giaccherini had another chance to grab a second for his side shortly before the interval as he collected the ball on the edge of the box, only to fire his half-volley wide.
Conte's side did finally extend their lead just past the hour mark as Manuel Pasqual made an immediate impact off the bench, swinging a cross to the back post that Leonardo Bonucci converted with a powerful header.
Things almost got even better for the visitors in the 77th minute as Ciro Immobile released Zaza with a stylish flick, but the Sassuolo striker rattled the crossbar with his effort, while Alessandro Florenzi's rebound was saved by Nyland.
Zaza came close yet again shortly afterwards as he beat a defender before chipping an effort over the keeper, only for Vegard Forren to get back and clear the ball off the line.
There was no way back for Norway in the closing stages of the match as the visitors made a winning start to their Group H campaign.