Rossi put the Italians ahead in the 27th minute when he slotted home Domenico Criscito's cross from close range. Ukraine pushed for an equaliser and their task appeared a little easier when Davide Astori was sent off following a second booking with a quarter of an hour remaining.
However, it was Italy who claimed the second goal when Matri scored with nine minutes remaining to confirm the win.
Italy beat Slovenia on Saturday as they took control of UEFA EURO 2012 qualifying Group C, but it was the hosts who threatened first tonight, Yevhen Seleznyov and Artem Fedetskiy both testing Emiliano Viviano in the Italy goal.
Criscito and Rossi both had shots comfortably held by Olexandr Shovkovskiy before the latter gave the Azzurri the lead in the 27th minute. Criscito crossed from the right and the Villarreal forward slotted a left-footed shot low into the bottom-left corner of the goal.
The open nature of the game continued in the second half as Daniele Gastaldello blocked Yaroslav Rakitskiy's 20-yard shot with Igor Oschypko sending a close-range shot wide from the resulting corner. Fedetskiy sent in a right-footed effort from 20 yards which Viviano pushed out for a corner as the hosts pushed for an equaliser.
They were given greater hope when Italy were reduced to ten men after Astori, a 17th-minute replacement for the injured Giorgio Chiellini, was sent off following a second bookable offence with 15 minutes left.
Marko Devic then had a shot before Viviano was forced to parry Oleg Gusev's right-footed effort. It was Italy, though, who scored the second goal of the night when Sebastian Giovinco provided a pass from the left side of the area which Matri swept into the bottom-left corner with nine minutes to go.