Switzerland picked up a 4-0 victory away to Lithuania, which means they are now joint top of the World Cup qualifying group, but Italy still have a better goal difference.
Breel Embolo scored twice, with Renato Steffen and Mario Gavranovic also on target in Vilnius this evening.
That allowed Switzerland to catch up to Italy, so both teams now have 14 points with six games played.
Only the group winners go through directly to the 2022 World Cup in Qatar, as the runners-up must enter the play-offs.
Italy and Switzerland go head-to-head at the Stadio Olimpico in Rome on November 12.
The Azzurri still have the upper hand due to a superior goal difference, although this 4-0 result did eat into it somewhat.
Italy have a goal difference of +11, while the Swiss are now on +9.
After that showdown, Italy visit Northern Ireland on November 15 and Switzerland host Bulgaria that same evening in the final qualifiers.