The Azzurrini, having beaten England on matchday one, on Saturday thrashed hosts Israel 4-0 in Tel Aviv.
Riccardo Saponara gave Italy the lead after just 18 minutes and Israel's task was made all the more difficult when Eyal Golasa was sent off in the 37th minute.
Manolo Gabbiadini netted either side of half-time as Italy moved further ahead, before Alessandro Florenzi struck home to wrap up victory.
The win secures Italy's progression with a game to spare, with the only negative being an injury to Lorenzo Insigne.
In the earlier group game, England's elimination was confirmed as Norway secured a 3-1 win in Petah Tikva.
Efforts from Fredrik Semb Berge, Jo Inge Berget and Magnus Eikrem put Norway three goals up at Ha Moshava, before Craig Dawson got a consolation from the penalty spot.
The defeat condemns the Young Lions to an embarrassing group-stage exit for the second successive tournament and leaves Norway on course for the knockout stage.