Chifchieva, who is ranked 16th nationally in singles, defeated No. 95 Daria Petrovic 5-7, 6-3, 6-3 while Haney defeated Alejandra Guerra 4-6, 7-6 (7-5 tiebreaker) and 6-3.
The Tigers, the surprise team of the SEC this year, improved to 14-9 overall while N.C. State finishes the season 13-11.
"I can't say enough about the effort these girls gave today," second-year Auburn coach Tim Gray said. "With our backs up against the wall, these players responded and played great tennis."
Auburn dug itself into a hole by losing the doubles point as Gray changed his normal lineup, not using Whitney Chappell, who normally plays No. 4 singles and two doubles.
AU's No. 3 player, Melissa Koning, tied the match at 1-1 with a straight sets 6-1, 6-3 victory over Berkeley Brock. The Wolfpack regained the lead when AU's Kelly Adams, who normally plays No. 6, was a 6-1, 6-3 loser to Kate Green No. 5 singles. Heather Bybee, who was 0-4 in singles, took over the No. 6 spot and lost 6-1, 6-2 to Neils Barringer.
Auburn cut the lead to 3-2 when Jill Hastenrath, who normally plays at No. 5, picked up her first No. 4 singles victory in three tries with a 6-4, 6-2 victory over Julia Roach.
With the one and two singles matches in the third sets, the action moved indoors after a lightning delay and Auburn closed out the Wolfpack with two more singles wins, first by Haney and then by Chifchieva.
The Tigers will be a major underdog on Sunday in round two vs. Georgia, a team the Tigers lost to 4-1 in the SEC Tournament after upsetting UGA 4-3 in the regular season at Auburn. UGA cruised to a 4-0 opening round victory over South Carolina State.
In the men's competition, the Tigers and Bulldogs competed indoors after a two-hour rain delay at the outdoor courts. Auburn finishes its season with a 15-10 record that included an opening round NCAA Tournament 4-0 win over Georgia State on Friday.
Georgia built momentum by winning the doubles point. Top-ranked Luis Flores and John Isner defeated No. 39 Robbert Lathouwers and Alex Schweizer, 8-5. Court three decided the doubles point as Georgia's Jamie Hunt and Nate Schnugg got past Lukas Marsoun and Alexey Tsyrenov, 8-3.
1. #16 Fani Chifchieva (AUB) def. #95 Daria Petrovic (NCSU) 5-7, 6-3, 6-3
2. Alex Haney (AUB) def. Alejandra Guerra (NCSU) 4-6, 7-6 (7-5), 6-2
3. Melissa Koning (AUB) def. Berkeley Brock (NCSU) 6-1, 6-3
4. Jil Hastenrath (AUB) def. Julia Roach (NCSU) 6-4, 6-2
5. Kate Green (NCSU) def. Kelly Adams (AUB) 6-1, 6-3
6. Neils Barringer (NCSU) def. Heather Bybee (AUB) 6-1, 6-2
1. Alejandra Guerra/Daria Petrovic (NCSU) def. #13 Alex Haney/Melissa Koning (AUB) 8-4
2. Kate Green/Julia Roach (NCSU) def. Kelly Adams/Jill Hastenrath (AUB) 8-5
3. Kristen Bleakley/Berkeley Brock (NCSU) vs. Heather Bybee/Fani Chifchieva (AUB) 6-6, unfinished
1. #1 Luis Flores/John Isner (UGA) def. #39 Robbert Lathouwers/Alex Schweizer (AU), 8-5 2. #16 Travis Helgeson (UGA) vs. Pawel Dilaj/Terence Nugent (AU), 5-2, uf 3. Jamie Hunt/Nate Schnugg (UGA) def. Lukas Marsoun/Alexey Tsyrenov (UA), 8-3
1. #1 John Isner (UGA) def. #56 Alex Schweizer (AU), 7-5, 7-6
2. #14 Luis Flores (UGA) def. #39 Robbert Lathouwers (AU), 6-4, 6-0
3. #12 Travis Helgeson (UGA) def. Lukas Marsoun (AU), 6-0, 5-7, unfinished
4. #35 Matic Omerzel (UGA) def. Alexey Tsyrenov (AU), 6-4, 6-2
5. Pawel Dilaj (AU) vs. #95 Nate Schnugg (UGA), unfinished
6. Terence Nugent (AU) vs. #104 Jamie Hunt, unfinished