The Azzurri equalled Spain's European mark with a 1-1 draw against Bulgaria earlier this week and are now level with Brazil's global record, set between 1993 and 1996.
But the point will be considered a disappointment by Roberto Mancini as Jorginho missed a penalty and the wasteful visitors squandered a number of other presentable opportunities.
The draw leaves Italy, who had scored in each of their previous 17 matches, top of Group C and four points better off than a Switzerland side with two games in hand to play.
Domenico Berardi was reinstated in Italy's starting line-up and wasted the best of the first-half chances when failing to beat Yann Sommer after being played clean through.
Lorenzo Insigne was denied from a free-kick by Sommer, who was also equal to a weak shot from Ciro Immobile after Manuel Akanji had glanced just over at the other end.
An annoyed Mancini's mood did not improve eight minutes into the second half as Jorginho's tame penalty, awarded for Ricardo Rodriguez's foul on Berardi, was easily saved by Sommer.
That was the first penalty Jorginho has missed for Italy at the sixth time of taking one, excluding shoot-outs, having missed one in the Euro 2020 final against England.
Mancini instantly turned to substitutes Federico Chiesa and Nicolo Zaniolo but Italy struggled to create many more openings, with Insigne not getting enough power behind his shot to beat Sommer from the best of those.