The 76th-ranked Swiss took the biggest upset victory of her career, defeating four-time Grand Slam champion Osaka by 3-6, 6-3, 6-3 at the final major US Open tuneup tournament.
Teichmann took just over two hours to defeat Osaka, breaking the Japanese star three times in the final set to reach the quarter-finals.
Osaka made 41 unforced errors in the match while hitting only 17 winners while Teichmann struck 21 winners against 29 unforced errors.
Ashleigh Barty (AUS x1) bt Victoria Azarenka (BLR x14) 6-0, 6-2
Barbora Krejcíková (CZE x9) bt Garbiñe Muguruza (ESP x8) 6-1, 6-7 (5/7), 6-2
Angelique Kerber (GER) bt Jelena Ostapenko (LAT) 4-6, 6-2, 7-5
Petra Kvitova (CZE x11) bt Ons Jabeur (TUN) 6-1, 6-2
Karolína Plísková (CZE x5) bt Jessica Pegula (USA) 6-4, 7-6 (7/5)
Paula Badosa (ESP) bt Elena Rybakina (KAZ) 6-2, 7-6 (7/5)
Belinda Bencic (SUI x10) bt Karolína Muchová (CZE) 7-5, 2-1, retired