Juventus made nine changes from their weekend win over Bologna, with Cristiano Ronaldo left out of the matchday squad entirely.
It was one-way traffic from the off, with Alvaro Morata stinging the palms of SPAL goalie Etrit Berisha in the eighth minute.
Juve won a penalty with a quarter of an hour gone after Adrien Rabiot was fouled in the box. Morata converted from the spot for the opener.
In the 33rd minute, Kulusevski did brilliantly by turning Ranieri inside out and then pulling the ball back into a dangerous zone. Fagioli left it and Gianluca Frabotta picked his spot past Berisha to double the lead.
SPAL were not down and out just yet. Floccari profited from some poor play from Demiral by carrying the ball forward and shooting wide from 20 yards.
In the 55th minute, Kulusevski wriggled clear of a couple of players but his low shot did not have enough precision to beat Berisha.
Kulusevski made certain of Juve's place in the semi-finals in the 78th minute with a composed finish past Berisha after being played in by Federico Chiesa.
Cosimo Marco da Graca was denied by Berisha from a half-volley but Juve added a fourth goal to their tally from the next attack as Chiesa rounded Berisha and walked the ball into the back of the net.