Following her breakthrough win over Maria Sharapova on Wednesday, the Australian was out of sorts in her 6-2 6-2 round-robin loss to the clinical Belarussian at Istanbul's Sinan Erdem Arena.
It was the Queenslander's fifth straight defeat against Azarenka - yet to drop a set to Stosur.
The result means the reigning US Open champion must defeat Li Na in her final-round robin match to be a good chance of reaching Saturday's semi-finals in the elite eight-woman competition.
The top two players from each group advance to the semi-finals of the $US4.9 million ($A4.7 million) tournament.
Having played so well to snap a nine-match losing streak against Sharapova, Stosur was a shadow of herself against another scream queen on Wednesday.
Inglis
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova
Maria Sharapova