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A Breel Embolo penalty had broken the deadlock for Switzerland early in the first half in Santa Clara, before the Swiss were made to pay by a Miro Muheim own goal.
Qatar, appearing in just their second finals after hosting the 2022 World Cup, looked rusty after their preparations were disrupted by the Middle East war, meaning their meeting with Switzerland was just their third match since December last year.
And for the majority of the match they were outclassed as Switzerland racked up 26 shots, before the unfortunate Muheim put through his own net under intense pressure from Qatar captain Boualem Khoukhi four minutes into injury time to spark wild celebrations on the Qatar bench.
"I am very proud of the team," said Qatar's Spanish coach Julen Lopetegui.
"I told them that even if we hadn't scored the goal and didn't draw I would have been proud of the mentality and discipline that they showed today.
"But fortunately we scored and that was history."