Breel Embolo gave Switzerland the lead on a penalty in the 17th minute.
The Rennes striker placed the ball into the left corner while Qatari goalkeeper Mahmoud Abunada rushed to the other side.
It was Embolo's 25th goal in his 87th cap.
Switzerland dominated, but struggled for efficiency.
It paid off. Boualem Khoukhi equalized with a header in the fourth minute of added time.
Qatar, who are making their second World Cup, lost all three of their matches in the home World Cup four years ago - but now took their historic first point.
Many empty seats dotted the stadium in Santa Clara, California. The International Football Federation FIFA was accused of trimming the attendance figures for the South Korea-Czech Republic match the other day, but it said not all spectators took their seats and were elsewhere in the stadium area.
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