Switzerland were made to wait to secure qualification for next year's European Championship as Shon Weissman's 88th-minute strike salvaged a 1-1 draw for Israel in Felcsut on Wednesday.
Ruben Vargas netted in the 36th minute to put the Swiss on track to seal the three points they needed to qualify from Group I with two games to spare, but they could not hold on.
Murat Yakin's Switzerland could still book their place in Germany for Euro 2024 with a win against Kosovo on Saturday.
Israel, playing home matches in Hungary due to the nation's war against Hamas in Gaza, still likely need to beat Romania on Saturday to remain in contention for a top-two finish and automatic qualification.
The Swiss, knowing victory would send them to a sixth straight major tournament, made a fast start, with Vargas going close and Noah Okafor hitting the post.
Augsburg midfielder Vargas headed home to put his side ahead, before then also striking the crossbar.
Israel belatedly improved in the second half, with Anan Khalaili's header coming back off the bar.
Weissman came to the rescue with two minutes of normal time remaining, with his goal being confirmed after a VAR check.
Edimilson Fernandes was sent off late on for Switzerland and will be suspended for the game against Kosovo in Basel.
