Elsewhere Turkey beat Sweden and Scotland defeated Albania
Fernando Santos’ men did not have to get out of second gear to take the points against a much-changed side fielded by Roberto Mancini in the Group A3 clash in Lisbon.
After a dominant first-half display, the hosts finally made the breakthrough at the start of the second half when Sevilla loanee Andre Silva curled a shot into the bottom corner in the 48th minute.
Italy created their best chance 12 minutes from time but Simone Zaza could not get his header on target.
Two late goals from Emre Akbaba snatched Turkey a dramatic 3-2 win against Sweden in their Group B2 encounter.
Isaac Kiese Thelin opened the scoring for Sweden, turning in the rebound after his header had come back off a post.
Viktor Claesson made it two with a thumping 30-yard strike, only for Hakan Calhanoglu to pull one back shortly afterwards with a low drive from the right of the area.
It was 2-2 after 88 minutes when neat interplay ended with Akbaba lashing the ball into the roof of the net, and there was still time for the Galatasaray midfielder to head home a winner in the second minute of stoppage time.
Scotland claimed an encouraging 2-0 win over Albania in their Group C1 clash at Hampden Park.
Alex McLeish’s side had suffered a chastening 4-0 defeat by Belgium on Friday night but bounced back in their opening fixture, taking the lead two minutes after the break when Steven Naismith’s header went in off defender Berat Xhimshiti.
The Hearts attacker, a late call-up, headed in a second in the 68th minute to clinch three points and a welcome win for McLeish, whose side went into the game with one win in five friendly matches and having scored only one goal.
Fulham striker Aleksandar Mitrovic bagged a brace as Serbia were held to a 2-2 draw at home by Romania in Group C4.
He bundled in the first from on the floor, while his second, after Nicolae Stanciu had levelled from the penalty spot, was lashed home on the volley after the ball had sat up nicely in a crowded penalty area.
George Tucudean turned the ball home at the near post from a corner to grab Romania a point.
In the same group, goals from Stefan Savic and Marko Jankovic earned Montenegro a 2-0 win over Lithuania.
In Group D1, Andorra drew 1-1 with Kazakhstan and in Group D3, Sheffield Wednesday striker Atdhe Nuhiu helped Kosovo to a 2-0 win over the Faroe Islands and Malta drew 1-1 at home to Azerbaijan.