Italy equalled the international record of 36 unbeaten games but were held to a draw in Switzerland that keeps World Cup qualifying Group C in the balance.
The European champions were the better side but also wasteful, with Jorginho seeing a second-half penalty saved.
Roberto Mancini's side top the group with 10 points, four points ahead of the second-placed Swiss but having played two matches more.
Elsewhere, Germany and Spain both recorded big wins to top their groups.
And that is where Italy find themselves after securing a second successive draw, but one that gives them a place in the record books, ahead of the 35-game run of Spain (2007-09) and level with the 36 games without defeat set by Brazil between 1993 and 1996.
Chelsea midfielder Jorginho's spot-kick was the Azzurri's golden chance to seal the win and return to winning ways after their disappointing 1-1 home draw with Bulgaria on Thursday.
But his effort was saved by Yann Sommer, who guessed correctly to block down to his left after Domenico Berardi had been fouled by Ricardo Rodriguez.
The next Group C games are on Wednesday, with Italy hosting winless Lithuania and Switzerland travelling to face the side placed third in the group, Northern Ireland.
Germany and Spain rediscover their edge
After labouring to a 2-0 win over Liechtenstein on Thursday, Germany rediscovered their ruthless edge in a 6-0 demolition of Armenia to reassert their authority in Group J.
Serge Gnabry netted twice in the opening 15 minutes and Marco Reus and Timo Werner both scored before the break as they dismantled the Armenian defence.
Jonas Hofmann added a fifth seven minutes after the break with a low bouncing drive, and substitute Karim Adeyemi put the icing on the cake with a goal on his international debut in stoppage time.
The win means the Germans leapfrog Armenia to the top of the group, with their visitors now two points behind in second spot. Romania are third on nine points, one ahead of North Macedonia.
Spain got back to winning ways as they thrashed Georgia 4-0 to go top of Group B, although their place remains a precarious one.
Luis Enrique's side have 10 points from five games but have played two more than second-placed Sweden, who have a 100% win record from their three matches, which includes Thursday's 2-1 win over the Spanish.
On Sunday, Jose Gaya, Carlos Soler and Ferran Torres put the hosts in control as they showed no hangover from that loss in Solna - their first World Cup qualifying defeat in 28 years.
Pablo Sarabia added another after the break as Luis Enrique's side cruised to three points.
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