Bayer Leverkusen winger Wirtz crashed in a 20-metre effort when the ball was played upfield from kick-off.
Arsenal midfielder Kai Havertz slotted in from close range early in the second half on Saturday as Julian Nagelsmann's side inflicted another defeat on Les Bleus, having also won a friendly in Dortmund in September.
Brazil's 17-year-old forward Endrick scored a late goal to beat England 1-0 at Wembley.
The Palmeiras youngster, set to join Real Madrid in the summer when he turns 18, slotted in his first international goal with 10 minutes left after Vinicius Jr's shot had been saved following a swift break.
Gareth Southgate's Euro 2024 hopefuls suffered a first defeat since the 2022 World Cup quarter-final against France.
Austria also made a fast start to their game in Slovakia, scoring after only six seconds in a 2-0 win in Bratislava.
RB Leipzig forward Christoph Baumgartner fired Austria in front following a driving run and low shot straight from kick-off.
Andreas Weimann added a late second for Austria, who will be in Group D with France and the Netherlands at Euro 2024.
The Republic of Ireland battled to a 0-0 draw with Belgium at the Aviva Stadium in a first game for interim manager John O'Shea.
Brighton forward Evan Ferguson saw a first-half penalty saved by Belgium goalkeeper Matz Sels.
Belgium - without Romelu Lukaku and Kevin De Bruyne - almost snatched a late winner when a low shot from substitute Thomas Meunier was pushed around the post by Liverpool goalkeeper Caoimhin Kelleher.
It also finished goalless between Denmark and Switzerland at Parken Stadium in Copenhagen.
Croatia beat Tunisia 5-4 on penalties after a goalless 90 minutes in Cairo, where they are playing in a four-team friendly tournament also involving hosts Egypt and New Zealand.
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