His omission appeared to hamper the hosts during the first half, with their best chance falling to Karim Benzema eight yards from goal.
The French striker's effort appeared bound for the back of the net, but visiting goalkeeper Kiko Casilla stuck out his hand to send the ball over the crossbar.
© Getty Images
The deadlock was eventually broken in the 64th minute, though, through Gareth Bale. The Welsh winger raced onto a through-ball from Benzema, before he slotted the ball inside Casilla's far post.
Morata then doubled the advantage in the 85th minute when he converted Angel di Maria's low cross and although Pizzi reduced the arrears moments later, Morata made sure of the outcome in stoppage time with an almost carbon copy of his first goal.