Italy's win leaves them in second place ahead on goal difference of Ukraine, who won 2-0 against North Macedonia.
Both teams have 10 points but Italy have a match in hand on all their group rivals except England, who top the group with 13 points.
Hungary remain top of Group G after beating second-placed Serbia 2-1, with all the goals coming in the first half.
Hungary have 13 points, three points above Serbia with a game in hand.
They are level on 16 points with second-placed Denmark, who won 3-1 at home to Kazakhstan.
Persons:
Domenico Berardi, Luciano Spalletti's, Ciro, Lorenzo Pellegrini, Mateo Retegui, Federico Chiesa, Sandro Tonali, Nicolo Zaniolo, Italy's, Giacomo Bonaventura, Bonaventura, Davide Frattesi, Spalletti, Gareth Southgate's, Benjamin Sesko, Erik Janza, Tommy Lund, Anita Kobylinska, Ken Ferris
Organizations:
Malta, Italy, Stadio San Nicola, North, Sky Sports, RAI Sport, England, Wembley, H, Slovenia, Thomson
Locations:
Italy, Hungary, Germany Slovenia, Denmark, England, Slovenia, Bari, Malta, Germany, Turin, Ukraine, North Macedonia, ENGLAND, Serbia, Lithuania, Finland, Kazakhstan, Gdansk