The 17-year-old has captured the imagination of the public by rolling over Anastasia Pavlyuchenkova, fourth seed Elena Dementieva and 2006 champion Maria Sharapova.
On day eight of the hardcourt major, Oudin again whipped up the packed Arthur Ashe Stadium into a frenzy when she fought back from a set down to toss Petrova on to the Flushing Meadows scrapheap.
Backed by 23,000 screaming fans, Oudin sealed victory by belting a forehand winner on her third match point.
She will next face either a fifth successive Russian, French Open champion Svetlana Kuznetsova, or Danish ninth seed Caroline Wozniacki for a place in the semis.
Kuznetsova upset, Mauresmo injured
Sania in second round at Wimbledon
Sania-Chuang in final of MPS Group Championships
Sania in semis of Pattaya Open
Bartoli ousts Wozniacki in Stuttgart