Across Europe, Hungary and Italy were battling it out to top the group and qualify for the Nations League finals next year.
It was the visitors who struck first as a defensive mishap allowed Giacomo Raspadori to nip in and walk the ball into an empty net.
The Azzurri doubled their advantage in the second half with a wonderfully crafted team goal which ended with Bryan Cristante setting up Federico Dimarco at the back post to tap in.
Hungary did register more shots on targets than Italy, but the understrength European champions comfortably kept them at bay.
They join Croatia and the Netherlands in qualifying for the finals scheduled for next year. Either Portugal or Spain will make up the quartet, with the deciding fixtures in Group 2 to take place on Tuesday.