On 20 June 2014, Sassuolo bought Zaza outright from Juventus for another €7.5 million. Juventus, however, retained the right to re-purchase Zaza for a reported €15 million by 30 June 2015 and €18 million by 30 June 2016.
On 31 August 2014, he was called up by head coach Antonio Conte as part of the senior team squad for a friendly match against the Netherlands and the first UEFA Euro 2016 qualifying game against Norway. On 4 September, Zaza made his debut with the Italian national team, playing as a starter in a 2–0 win against the Netherlands. He was fouled by Bruno Martins Indi in the ninth minute to win the penalty kick from which Daniele De Rossi scored Italy's second goal in the 2–0 victory. On 9 September, Zaza scored his first goal for the Italian national team in the 16th minute of their opening Euro 2016 qualifier against Norway, of a 2–0 victory. On 31 May 2016, he was named to Conte's 23-man Italy squad for Euro 2016. On 17 June, he came off the bench to set-up Éder's match-winning goal against Sweden in the 88th minute of his nation's second group match, which qualified Italy to the Round of 16. On 2 July, he was brought on in the last few seconds of extra-time to take a penalty in the resulting penalty shoot-out against Germany in the quarter-final match up, which he subsequently missed after a bizarre run up to the ball, as Italy were defeated in the shoot-out 6–5 and eliminated from the tournament. In the events after the match, Zaza issued an apology to the fans of the national team stating, "I am sorry to have let the Italian people down. I missed the most important penalty of my life and I will carry this burden with me forever ... I have always taken penalties like that and I was convinced I would score, I had sent him [Manuel Neuer] the wrong way but the ball set off and it went like that."