Kyra Cooney-Cross dream goal helps Matildas beat Germany - ESPN

Kyra Cooney-Cross has marked her 50th cap with a wonder goal and Clare Hunt also netted a maiden international header to gift Australia the most unlikely, party-pooping 2-1 triumph over Germany in Duisburg.

The 26,000-strong crowd had come to pay an emotional farewell to their departing heroine Alexandra Popp at the MSV Arena on Monday evening (Tuesday AEDT) but ended up having applaud a glorious piece of party-pooping by Arsenal midfielder Cooney-Cross who fired home a first-half equaliser from all of 40 yards.

It was an astounding strike against the run of play six minutes before half-time after Selina Cerci's fifth-minute opener for the dominant hosts.

Yet though Germany continued to largely run the show throughout, the never-say-die Matildas held firm, grew stronger and pounced again, central defender Hunt heading home a winner from captain Steph Catley's corner in the 79th minute.

It earned Australia their first win against the world's No.4 side Germany in 19 years, and only the second victory in their history over one of football's powerhouse nations.

The first international goals for the two London-based Matildas also conjured up another remarkable triumph for caretaker boss Tom Sermanni's side, who had been hammered by Germany 3-0 in Marseille during their woeful Olympics campaign just three months ago.

The 70-year-old Scot had also been in charge for Australia's last win over Germany.

Yet a win had looked a pipedream after a nightmarish start following the pre-match presentation to Popp, who made a cameo appearance for her 145th and final cap.

Her teammates seemed determined to celebrate the 33-year-old Olympic great, striking after just five minutes when the Matildas gave the ball away in midfield, the Germans countered down the right and Vivien Endemann's cross was met by a soaring, unmarked close-range header from Selina Cerci.

Full-back Felicitas Rauch hit the post with a speculative strike, Popp had a close-range free-kick blocked and the hosts looked as if they might score on every attack.

Skipper Popp took her leave after just 15 minutes, leaving the field to a cheering, standing ovation as the hugs and tears began to flow - but it didn't stop the flow of home attacks and chances.

Yet the shackles were unexpectedly broken by excellent lone striker Caitlin Foord, who was set free twice in the space of three minutes from neat through-balls delivered by Cooney-Cross and a much busier Mary Fowler, only for the Arsenal forward to be thwarted by German keeper Stina Johannes.

Apart from those two efforts, the visitors only had one other shot on goal in the first half compared to the Germans' 14 - but what an effort it was, a stupendous goal that 22-year-old Cooney-Cross will never forget on her landmark night.

After Endemann had been robbed in her own half, the ball fell to the Queenslander, who saw Johannes off her line and hit a perfectly struck shot that arched over the desperate, back-pedalling keeper into the net.

Still Germany attacked, Endemann missing a sitter and Sjoeke Nusken also should have scored.

The injured Kaitlyn Torpey had to be replaced, with Michelle Heyman brought on to lead the line and Foord dropping back. The enforced change seemed to make the Matildas more solid and competitive in that formation after the break.

The visitors were helped too by Germany using the match to experiment, with six changes to their starting line-up and six more made before the hour mark, but Australia increasingly clawed their way back with Foord a titan with her foraging work up front and also in defence.

Rusty sub Heyman had to come off in the second half as Sermanni gave an international debut to Brisbane Roar's Winonah Heatley, who got booked for a foul within two minutes.

Germany ended with 18 shots on goal to the Australians' six, but keeper Mackenzie Arnold was a tower of strength, pulling off one last key save at full-length to deny sub Pia-Sophie Wolter's left-foot strike in the 79th minute.