The striker latched on to Leonardo Bonucci's perfect pass to finish past Thibaut Courtois before Pelle struck in injury time, as Antonio Conte's men notched a proficient win
Italy sprung a surprise in Group E by beating Belgium as Euro 2016's highest-ranked nation fell to a 2-0 loss in Lyon.
Marc Wilmots' side, who sit second in the FIFA rankings, had been considered by many as favourites to prevail in France, but they have work to do following Monday's damaging defeat.
Emanuele Giaccherini opened the scoring with a superb two-touch finish following a stunning pass from Leonardo Bonucci.