Baumgartner went into the record books during a friendly match in Bratislava. The Leipzig attacker drove through the home defence from kick-off before unleashing a 25-metre shot past Martin Dubravka in goal.
"We've done this variation before, sprinting from kick-off at full risk. The sequence of steps somehow worked out so that I made the run," Baumgartner told Austrian public broadcaster ORF after the game which his team won 2-0.
"Of course it's really cool, I'm very happy. The fact that I hit it like that... it's of course sensational."
Baumgartner's strike matched the seven seconds it took Lukas Podolski to score for Germany against Ecuador in May 2013.
The Austrian FA described Baumgartner's effort as the fastest goal in the history of international football.
"Of course we got off to a really good start, that goal by itself was probably worth the price of admission," said Austria coach Ralf Rangnick.
Meanwhile, later on Saturday, Wirtz was just as fast against France in a friendly in Lyon.
The Leverkusen player beat goalkeeper Brice Samba with a superb shot under the crossbar.
The fastest goal scored in a World Cup was by Turkey's Hakan Sukur against South Korea in 2002 after 11 seconds.
