The hosts got off to a lively start, with William Carvalho heading wide inside the opening minutes, although the midfielder was flagged offside.
Portugal went close to taking the lead in the 27th minute when Carvalho picked out Bernado Silva, who saw his drilled effort cleared off the line by Alessio Romagnoli.
The woodwork came to Italy's rescue four minutes later when Mário Rui's deflected effort hit the woodwork with Gianluigi Donnaruma well beaten.
The Italians were struggling to deal with the European champions, who went close to scoring in the 36th minute with Carvalho drilling a low strike inches wide of Gianluigi Donnaruma's goal.
Portugal picked up from where they left off in the first half and took the lead three minutes after the break, with Andre Silva firing past Donnarumma from close range.
Mancini responded with a change on the hour mark as Ciro Immobile made way for Domenico Berardi as the visitors went in search of an equaliser.
The visitors managed to carve out an opening with 12 minutes remaining but Zaza Simeone failed to direct his header on target from close range.
Substitute Emerson managed to create an opening for Italy in the 83rd minute, whipping a free-kick into the box that found Mattia Caldara, who headed off target.
That proved to be the final chance as the European champions held on to claim three points.
Sweden 2-3 Turkey