Italy failed to qualify for both the 2018 World Cup in Russia and then again in Qatar four years later, although they did win the European Championship, beating England in the final on penalties at Wembley, in 2021.
The match against Israel was held in Debrecen, Hungary and an own goal from Manuel Locatelli saw Italy go a goal behind in the 16th minute.
Former Everton striker Moise Kean equalised just before half-time, only for Dor Peretz to restore Israel’s lead early in the second half.
But the advantage only lasted two minutes before Kean grabbed his second before Matteo Politano put Italy ahead for the first time, with Giacomo Raspadori’s goal stretching the lead to 4-2 in the 81st minute.
Another Italian own goal, this time from Alessandro Bastoni, gave Israel hope in the 87th minute and two minutes later Peretz thought he had snatched a point for his side with his second goal in the 89th minute.
But Tonali grabbed the dramatic winner in what could be a vital three points for Italy.
Only the group winners are certain to qualify for next summer’s tournament in Canada, Mexico and the United States, with the runners-up entering the play-offs.
Italy play Estonia away on 11 October, entertain Israel on 14 October and then play in Moldova on 13 November before a potential group decider at home against Norway on 16 November.