Germany see off dogged Austria to reach Euro semi-finals
Lina Magull's (27) first-half strike and a late goal from Alexandra Popp (31) secured the win for Martina Voss-Tecklenburg's side but they found it tough going at the Brentford Community Stadium against an Austria side who hit the woodwork three times.
Austria, who reached the last four in the 2017 edition, started strongly and came close to opening the scoring in the 13th minute when Marina Georgieva (25) rose to meet a corner but her header hit the outside of the post.
Germany took the lead in the 26th minute after a poor kick out by goalkeeper Manuela Zinsberger (26) was headed up to Klara Buhl (21) who surged to the byline and cut it back for Popp who stepped over the ball, leaving it for Magull to score.
Austria fought back in the second half, forward Barbara Dunst (24) hitting the bar with an audacious long-range shot. Sarah Puntigam (29) also hit the post after her initial shot was blocked.
Germany soaked up the pressure and could have made the result safe in the 82nd minute but Buhl somehow missed a tap-in in front of an open goal.
She was not left to rue that miss as in the 90th minute Popp pressed keeper Zinsberger into hitting the ball against her and it ended up in the back of the net for her fourth goal of the tournament.
Germany will next play either France or the Netherlands who meet on Saturday.