They just missed out on second spot in Group C but advance as one of the four best third-placed teams, with Oday Dabbagh the hero for his two goals.
United Arab Emirates went through in second place despite losing 2-1 to group winners Iran.
The historic victory in Doha comes against the backdrop of the Israel-Hamas war in the Palestinian territory of Gaza.
"Thank you to the fans who are coming to support Palestine and the national team of Palestine. Thank you from our heart," captain Musab Al-Battat told beIN SPORTS after the game.
"We will do our best to put a smile for the people."
Oday Dabbagh setting the platform for
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