Niemeier, who is only playing her second Grand Slam tournament, beat Briton Heather Watson (109th) 6-2, 6-4 on Center Court.
At 22, she entered the world's top 100 players for the first time last May.
For her part, Maria, who has been back from maternity for less than a year, eliminated the Latvian Jelena Ostapenko (17th) 5-7, 7-5, 7-5.
At 34, Maria is the oldest player still in contention in the round of 16.
She had never previously passed the third round in Grand Slam, already reached at Wimbledon, in 2015.
To achieve this this year, she had beaten the Greek and world 5th Maria Sakkari, her first victory against a player from the World Top 10.
She herself was still beyond the 250th place in the world last March.
© 2022 AFP