A 3-0 loss to Norway in June left Italy's qualification campaign in trouble. More difficulties were in store when Israel twice took the lead in Monday's game played in Debrecen, Hungary.
Moise Kean found space among the Israeli defence to score each side of halftime, leveling the score on both occasions. Matteo Politano finally gave Italy the lead in the 59th minute off a backheeled flick assist from Mateo Retegui, and Giacomo Raspadori scored a fourth.
The game seemed over, but Israel scored twice in two minutes to level the score at 4-4, Dor Peretz scoring his second of the game.
Tonali then hit a speculative curling shot in the first minute of stoppage time which seemed unthreatening but found its way through a crowd of players and into the net.
Italian errors were a major topic, with two own goals and some glaring mistakes from new Manchester City goalkeeper Gianluigi Donnarumma.
"We're crazy - we conceded some absurd goals but we will hold onto this win," said Italy manager Gennaro Gattuso following his second game in charge.
"Our opponents surprised us a bit, they were marking man-to-man.Â
"We're too fragile, we give away goals too easily. The boys know it but the problem is mine, not theirs."
Italy moved ahead of Israel for second place in Europe Group I. Norway stayed top with four wins from their four games and face last-placed Moldova on Tuesday.
Sweden's qualifying bid is already struggling after a 2-0 loss to Kosovo left the Swedes with one point from their first two games. Kosovo scored both goals on lightning-fast counterattacks which began in its own penalty area.
Switzerland stayed top of Group B after beating Slovenia 3-0 with two of their goals coming from headers at corners.
Denmark and Scotland were level on four points at the top of Group C after the Danes beat Greece 3-0 and Scotland won against Belarus 2-0.
Croatia eased past Montenegro 4-0 to top Group L after Montenegro's Andrija Bulatovic was sent off for two bookings in the space of eight minutes before halftime.
Croatia are level on points with the second-placed Czech Republic but have played one less game. The Faroe Islands beat Gibraltar 1-0.
