It was a tighter game than many would have expected as Germany faced their biggest test yet in their pursuit of a record-extending ninth European title.
Klara Buhl hustled the ball from an Austrian defender and crossed into the box where Alexandra Popp, on for her fourth goal in four games, unselfishly left the ball to the arriving Lina Magull who slotted home to open the scoring.
Popp got her moment in the dying minutes of the match as Austria goalkeeper Manuela Zinsberger's attempt to play out from the back backfired and Popp stuck a boot out to nudge into the net.
The Wolfsburg forward has scored in four consecutive Euro matches, equalling the record of Heidi Mohr who did so between 1989 and 1993, and moves within one goal of England's Beth Mead in the battle for the Golden Boot.
"It was a very intense game - Austria was very hard to play against. I'm happy to finish my fourth goal and happy and proud of the team," said Popp.
"At the beginning we were not the top favourite and now we've shown all the world where we are. I think the team spirit is very important for us and that's the point where we're so strong and we hope the history has not ended."
Despite having earned 117 international caps, this is Popp's first Euros tournament after returning from a long-term injury which kept her sidelined for 10 months in the build-up to the competition.
"I had a very hard time last year [with injury] - I'm very thankful to be here. I'm free, I feel good and I can help my team," she said.
"We're very happy to have very many fans here. We need the spirit, the support and that's a very good feeling. We also feel the support from Germany - we'll give our all to get to the final."
Martina Voss-Tecklenburg's side benefited from an element of luck against Austria but will have plenty to work on before they face France or the Netherlands in the semi-final in Milton Keynes next Wednesday.
On paper it seems that Germany's Euro 2022 journey has been a straightforward one. And until now, it has been.
They had ample opportunity to extend their lead at 1-0, with Buhl shooting wide when faced with an open net after having a shot from distance denied, and Popp a persistent threat.
But their 100% record of clean sheets in the tournament - the only team left with such a return - flatters their occasional defensive frailty, as Germany struggled to assert the dominance they showed in the group stages and Austria missed big opportunities to draw level at 1-0.
Austria, featuring in just their second Euros, were surprise semi-finalists in 2017 but lost out on a place in the final to Denmark.
Irene Fuhrmann's side were unlucky - hitting the woodwork three times and putting their local rivals under more pressure than any other side so far.
"It's a hard moment right after the game," she said. "When we look back, the team can feel very proud of how they have played - not just today but throughout the tournament. We demanded everything from Germany."
These were only the second and third goals that Austria have conceded at this tournament - the first coming against England - but they have also only scored three goals and poor decision-making in the final third has cost them.
Despite having won the title on eight of the 12 occasions the Euros have been staged, Germany did not come into this tournament as outright favourites.
They lifted the trophy six times in a row between 1995 and 2013 but their bid for a seventh consecutive title was ended with a shock quarter-final defeat by eventual runners-up Denmark in 2017.
The absence of Lyon's injured midfielder Dzsenifer Marozsan and Chelsea's Melanie Leupolz, who announced her pregnancy in March, made it difficult to know what to expect but they seem to have grown as a team throughout the tournament.
-- Courtesy of BBC Sport