The 29-year-old Burger, wearing the armband in the absence of Bayern Munich’s Viktoria Schnaderbeck, struck after 15 minutes. Switzerland’s eventual late pursuit of an equaliser was handicapped by the sending-off of central defender Rahel Kiwic.
Burger was again the unwitting cause, being pulled around by Kiwic on the edge of the penalty box. The red card was immediately produced by Bibiana Steinhaus who, next season, will become the first woman to referee in the men’s German Bundesliga.
The other Group C game saw France beat Iceland 1-0.
A crowd of 4,781 in the De Adelaarshorst stadium saw Switzerland make a second appearance on the international stage after the FIFA Women’s World Cup in Canada in 2015.
However it was Austria who dominated the opening exchanges, more to the point in the last third of the pitch and rewarded by taking the lead through Burger after only 15 minutes.
The Swiss game was more physical with captain Caroline Abbé booked in the 19th minute for a foul on Nicole Billa. After the first halfhour they claimed 66pc possession and a 73pc passing accuracy. But despite also possessing some experienced and high-quality players they seemed to lack the determination of their eastern neighbours.
Austria´s pressing game, as trainer Dominik Thalhammer had promised the previous day, did “frustrate” the Swiss players.
In the second half Switzerland´s trainer, Martina Voss-Tecklenburg, strengthening attack with the substitutions of defensive players Abbé and Fabienne Humm by midfielder Vanessa Bernauer and forward Eseosa Aigbogun.
However, then Kiwic was sent off and Voss-Tecklenburg, who retired from the German national team in 2000, had to readjust by bringing on defender Jana Brunner for forward Geraldine Reuteler.
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Bernauer and Ramona Bachmann both launched promising attempts at the Austrian goal but were denied by FC Bayern keeper Manuela Zinsberger.