The defending champions headed into the game trailing their second-placed rivals by five points in Group C following Saturday’s draw with North Macedonia.
But Frattesi’s double in the first 30 minutes gave the Italians valuable breathing space in Milan, despite Andriy Yarmolenko reducing the deficit before the break.
The win, Luciano Spalletti’s first as Italy coach, boosted their chances of qualifying for Euro 2024 after the misery of failing to reach last year’s World Cup.
They moved into second place, above Ukraine on head-to-head record — with the return match scheduled for next month.
The Azzurri have played a game less than Ukraine and England, who lead the group by six points.
ANSA