The competitiveness that willed Mark Price to an All-American career at Georgia Tech revealed itself again Saturday in Chapel Hill, N.C.

Caroline Price’s legs had cramped up, first her calf muscles, then her quadriceps and finally her hamstrings.

“I had never cramped before,” said Price, a North Carolina tennis player and daughter of the Tech basketball great. “I didn’t even know what was happening.”

In the style of her clutch-shooting dad, Price fought off four match points to win a third-set tiebreaker and clinch the Tar Heels’ 4-2 victory over Arizona in the second round of the NCAA women’s tournament.

“I just kept pushing,” said Price, a freshman. “I was like, I don’t want this to be the last match for my seniors.”

Price and her teammates will be one of 16 teams, including her father’s alma mater and Georgia, that will compete for the championship beginning Thursday. The men’s tournament, which includes Georgia, will start Friday, also at the Dan Magill Tennis Complex in Athens.

Price, a big-serving lefty who lately has played No. 4 or 5 singles and No. 3 doubles, has thrived for the seventh-ranked Tar Heels. She has a 29-13 record at singles and has gained an increasingly secure grasp on the college game. She is ranked 104th in the country.

“I think she’s just scratching the surface of how good she can be,” North Carolina coach Brian Kalbas said.

It’s a path she has been on since childhood. The second oldest of four Price children, Caroline grew up in Gwinnett County playing a lot of sports, including basketball. Her dad coached her one season, as a fifth-grader at Wesleyan.

“She was long, a very good defender. She needed some work on her shooting,” Mark Price said with a laugh. “That might have been the reason she went the tennis route.”

Caroline acknowledges the cardinal sin for a child of the NBA’s all-time free-throw percentage leader. She was “not very good” from the line.

“I was little, so my dad didn’t really worry about that much,” she said.

Caroline’s spontaneity draws a contrast with her father’s reserve. “She gets her personality from her mother,” Mark said.

She was won over by tennis, which her mother, Laura, played one season at Tech as a walk-on. Price had a standout junior tennis career, winning the 18s singles at the U.S. Clay Court championship in 2010 and the doubles title at the same event last year.

The benefit of having a dad who played at the highest level of his sport has proved far greater than his genes. She said he has helped develop her mental toughness, which has become a strength of her game, as her last match might attest.

“My dad is my hero, so everything he tells me, I listen to a lot,” Caroline said.

All along, she figured she would follow her parents to Tech. The Prices have been friends with Tech coach Bryan Shelton since he and Mark were at Tech together for two academic years.

Caroline grew up cheering for Tech’s football, basketball and tennis teams and said that it still felt like home when North Carolina came to Tech in March, winning 4-3. She ultimately deemed North Carolina the best fit, turning down Tech and Georgia.

Tech “was kind of the hardest one to say no to, for sure, because we love Bryan as a family and obviously, he’s a great tennis coach, too,” Mark said.

Caroline’s parents will make the trip from Orlando, where Mark recently finished his first season as player-development coach for the Orlando Magic, to Athens for the tournament.

Price plans to wear Carolina baby blue, a choice that has already earned him grief from neighbors when he’s biked around the neighborhood in a Tar Heels T-shirt.

Said Price, “But family trumps everything, right?”