Her run into the fourth round of the tournament is the deepest ever for an Auburn women's player in NCAA play.
Chifchieva, the SEC Player of the Year, posted a 6-4, 6-2 victory over Ani Mijacika of Clemson to advance into the quarter-finals that will be played on Saturday.
Chifchieva will face the No. 6 seed, Amanda Fink of Southern California, for a berth in the semi-finals.
"Fani picked up a great win," Auburn coach Tim Gray said. "She stayed focused and worked hard out there. Hopefully, she can carry that momentum into the quarter-finals."
Auburn's doubles team of Alex Haney and Melissa Koning couldn't advance to the third round on Friday as they fell 6-2, 6-7, 6-3 to Renata Kucerkova and Anastasia Petukhova of Fresno State.