With the win, UNC improved to 30-23, while the Seahawks fell to 21-28.
The shutout was the Tar Heels' seventh of the season and the fifth by freshman pitcher Ashley Allen, who struck out four and allowed five hits.
"Natalie Anter called a great game behind the plate and Ashley hit her spots," said UNC coach Donna Papa. "And it was exciting to have Tiffany break the record at home."
Tolleson, who is in her first year at UNC after transferring from Stetson, came into the game with 79 hits, one shy of the school-record of 80, held by Theresa Buscemi in 1992 and Christine Kubin in 1996.
A pair of bunt singles, on her first and third at-bats, pushed her season total to 81.
"I never thought when I came to UNC I'd get anything like this," Tolleson said. "It's cool. There's been some pressure the last couple of games as I got close to the record, so I'm glad to get it over with."
Tolleson also scored two runs to take her season total to 51, and needs just two more to break the school single-season record in that category.
She already holds UNC's single-season record for stolen bases and, with a total of 54 in 53 games, leads the NCAA in steals per game.
Tolleson led off the bottom of the first with her first single, stole second and moved to third on a sacrifice bunt by senior Rosie Gustavson.