The Paris Saint-Germain midfielder returned after a six-week knee injury layoff to help the Azzurri make it three wins out of three in the group stage against Wales last weekend.
Next up for Italy is a last-16 game against Austria in Wembley on Saturday.
The 28-year-old took the captain's armband when defender Leonardo Bonucci was substituted in the second half, with regular skipper Giorgio Chiellini sitting out the game with a muscular problem.
A delighted Roberto Mancini hugged Verratti as he left the pitch at the Stadio Olimpico, having surpassed expectations by playing the entire match in midfield alongside Jorginho.
Verratti and Jorginho are Mancini's first-choice midfield pairing, and having the duo in the driving seat again is a boost to Italy's hopes of lifting a trophy they have won once, back in 1968.