Morata headed an Andrea Barzagli cross past the helpless Sergio Rico on 41 minutes, before substitute Zaza doubled Juve’s lead with a late breakaway goal in the 87th minute.
Khedira was named in the starting lineup for the first time since his recent move from Real Madrid, and proved influential, giving Juve the kind of stability they have lacked in Serie A this season.
The victory establishes Juventus as the outright leaders in Group D with a maximum six points after two matches.
Sevilla and Manchester City, who beat Borussia Moenchengladbach 2-1 in the other Group D match on Wednesday, both have three points.
Juve's excellent form in Europe comes in stark contrast to their domestic woes, with last season's Champions League finalists having managed only one victory from their opening six fixtures.
They were much improved on Wednesday with Khedira in heart of the midfield, while two other new recruits, Paulo Dybala and Juan Cuadrado, both contributed to a menacing attacking display.