The match was originally scheduled to be played outdoors in Athens, Ga., at 9 a.m., but the rain forced a venue change to the indoor courts on the campus of Georgia Tech.
The Tar Heels will face either second seed Alabama or Notre Dame on Saturday at noon in Athens.
North Carolina (27-5) won an epic doubles match with Texas A&M (21-7) to earn an early 1-0 lead. After splitting on courts 2 and 3, the opening point came down to court one featuring the third ranked Tar Heel duo of Hayley Carter and Jamie Loeb.
Carolina led 5-1 before A&M ran off the next five points to take a 6-5 advantage, but Carter held serve to tie it up at 6-all. The Aggies also held for a 7-6 lead, before Loeb did the same to send the set into a tie breaker.
A&M led 2-1 and 4-2, before three-straight points gave UNC its first advantage in the breaker at 5-4. The Aggies later pulled in front 6-5 and served for the match, but the Heels held tight to tie it 6-all.
Still tied 7-7, Carolina won the next two points to secure the dubs point with an 8-7 (9-7) victory. Carter and Loeb improved to 17-0 this spring.
The 13th ranked tandem of Caroline Price and Whitney Kay breezed to an 8-2 win on court two to notch the other doubles victory for the Tar Heels.
In singles, Kay was the first to close out her match on court four, winning 6-2, 6-2 over Stefania Hristov for a 2-0 Tar Heel advantage.
Tessa Lyons made it 3-0 with a dominating 6-1, 6-1 victory over Mason Strickland on court six.
Top ranked Loeb clinched the 4-0 sweep with a 6-1, 6-3 win on court one over No. 10 Cristina Stancu, marking the second straight-set win over her this season.
The victory avenged an earlier season, 4-3, loss to the Aggies back in February in Chapel Hill, North Carolina.
WOMEN'S ROUND OF 16: #7 NORTH CAROLINA (27-5) def. #10 TEXAS A&M (21-7), 4-0 - Ken Byers Tennis Complex (Atlanta)
Doubles (Order of finish: 3,2,1)
1. #3 Jamie Loeb/Hayley Carter (NORTH CAROLINA) def. #14 Cristina Stancu/Stefania Hristov (TEXAS A&M), 8-7 (7)
2. #13 Whitney Kay/Caroline Price (NORTH CAROLINA) def. #79 Ines Deheza/Saska Gavrilovska (TEXAS A&M), 8-2
3. Rutuja Bhosale/Anna Mamalat (TEXAS A&M) def. #55 Tessa Lyons/Kate Vialle (NORTH CAROLINA), 8-3
Singles (Order of finish: 4,6,1)
1. #1 Jamie Loeb (NORTH CAROLINA) def. #10 Cristina Stancua (TEXAS A&M), 6-1, 6-3
2. #5 Hayley Carter (NORTH CAROLINA) vs. #56 Saska Gavrilovska (TEXAS A&M), 6-7(6), 0-1, unf.
3. #59 Caroline Price (NORTH CAROLINA) vs. Rutuja Bhosale (TEXAS A&M), 6-7(1), unf.
4. Whitney Kay (NORTH CAROLINA) def. Stefania Hristov (TEXAS A&M), 6-2, 6-2
5. #105 Ashley Dai (NORTH CAROLINA) vs. Anna Mamalat (TEXAS A&M), 6-4, 1-4, unf.
6. Tessa Lyons (NORTH CAROLINA) def. Mason Strickland (TEXAS A&M), 6-1, 6-1