Melli, one of the most sought- after young players in the Italian League after a successful season with the Italian Cup winners, Parma, scored from a goalmouth scramble in the ninth minute after the Kuwait defence had cleared a shot by Renato Buso.
Though Italy continued to pile pressure on the Kuwaitis, they could not get past goalkeeper Falah Al-Majidi. Melli had two headers deflected, and Pasquale Rocco missed from two first-half chances.
The victory takes the Italians into the last eight from Group A, behind the unbeaten group leaders Poland, who drew 2-2 with the United States earlier in the evening.
Qatar joined Spain from Group A despite having two men sent off and losing to Spain 2-0. Spain went through unbeaten as group leaders and without conceding a goal.
Francisco Navarez finished off Qatar with a goal from inside the penalty area in the 79th minute. Zamel Al-Kuwari was sent off in the 58th minute for two bookable offences, and Mubarak Nooralla was shown the red card a minute later.