Austria boss Ralf Rangnick said afterwards that this was the “most important match” he had faced since he took charge in April 2022.
Before their defeat to France, which was also the first time in almost two years they had failed to score, his side had lost only one of their 16 previous games.
Their form has seen them tipped to be this tournament’s surprise package and Baumgartner, who was named player of the match for his performance against Poland, felt that tag has helped rather than hindered them.
“Somehow it is nice to be called that,” Baumgartner said. “We had a really good period and people started to think big quite quickly, but we as a team knew how to assess the situation.
“We knew that against France we weren’t at our maximum but that’s what we need – if we do that, we can beat a lot of nations.
“So this pressure is mainly coming from ourselves because we know about our quality. It would have been a big, big shame if we had lost this game because it would have been tight for us then.
“We still have a lot of work in front of us but this victory was really important for us, and hopefully we can continue like that.”
Poland head coach Michal Probierz faced several questions about Lewandowski’s condition and revealed the veteran striker was fully fit, despite starting on the bench.
“He was fully fit and he has practised with the team,” said Probierz.
“We knew that this would be a highly intensive match and we decided with the medical team and Lewandowski himself that he wouldn’t start from the first minute.
“We wanted to get through that Austrian defence in the second half and it’s a pity we couldn’t score that second goal before them.”