The European champions scored the game's only goal 48 minutes in through Silva's well-taken shot, having knocked the door throughout the opening 45 minutes to no avail.
Victory over the Azzurri in the first competitive clash between the sides in a quarter of a century takes Portugal top of Group A3, two points in front of an Italian side with just one win to their name in nine outings.
Italy were criticised on the back of their 1-1 draw against Poland in their opening match in this competition, and their first-half showing here offered few positives for new boss Mancini.
In the absence of the rested Cristiano Ronaldo, Andre Silva led the line and had an early effort kept out by Gianluigi Donnarumma - one of the two surviving members from last time out, along with Jorginho.
Just three minutes of the second half were required for the Euro 2016 winners to open the scoring, though, with Andre Silva controlling Bruma's pass at the end of a swift counter and tucking it out of Donnarumma's reach.
Donnarumma could do nothing about that strike, but he was equal to Bernardo Silva's angled drive five minutes later, getting two strong hands to the ball to keep his side in the match.
Rather than pushing on from their deserved opener, Santos's men ceded possession all too easily and gave their opponents hope of rescuing a point.
Pizzi got a tame attempt on target 20 minutes from time, but shooting opportunities were proving to be few and far between at both ends of the pitch.
Despite struggling to keep hold of possession, the Azzurri may well have snatched something from the match late on as Simone Zaza headed a good opportunity over the bar.
The final chance of the match fell the hosts' way, with substitute Renato Sanches being kept out by the feet of Donnarumma, but it mattered little as Portugal made it 19 wins in 25 meetings with Italy.
PORTUGAL (4-3-3): Patricio; Cancelo, Pepe, Ruben Dias, Mario Rui; Pizzi (Sanches 74'), Ruben Neves, William Carvalho (Oliveira 84'); Bruma (Martins 74'), Andre Silva, Bernardo Silva
ITALY (4-3-3): Donnarumma; Lazzari, Caldara, Romagnoli, Criscito (Emerson 74'); Cristante (Belotti 79'), Jorginho, Bonaventura; Zaza, Immobile (Berardi 59'), Chiesa