The Azzurri remain ahead of the Swiss at the top of Group C on goal difference thanks to Giovanni Di Lorenzo's header which equalised Silvan Widmer's rocket opener for the away side.
However, passage to next year's tournament to Qatar is far from secure after Chelsea midfielder Jorginho blasted over a spot-kick in the final moments following a VAR check for a foul on Domenico Berardi.
Now the only two sides who can claim the group's single guaranteed qualifying spot head into their closing fixtures on Monday with it all still to play for.
Roberto Mancini's side travel to Northern Ireland while Switzerland, who recovered some pride at the Stadio Olimpico after being thumped at the same ground by Italy at Euro 2020, host Bulgaria.
Italy now have to match Switzerland's result to ensure a place in the World Cup, assuming that Switzerland fail to beat Bulgaria heavily enough to finish the group with the superior goal difference.
That leaves Italy facing the spectre of the playoffs, where in 2017 they failed to qualify for the World Cup for the first time in six decades following a miserable defeat to Sweden.
Widmer stunned the just under 50 000 crowd at the Stadio Olimpico with 10 minutes on the clock, meeting Noah Okafor's pull-back with a thumping strike that whizzed past Gianluigi Donnarumma and into the top corner.
The hosts were rocked and Switzerland could easily have been two ahead shortly after, with a goalmouth scramble being hastily cleared away and the bright Okafor then fizzing a low shot just past the upright.
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