McPhillips' No. 3 singles victory came after teammate Robin Anderson, the tournament's second seed, beat top-seeded Jamie Loeb, 6-2, 6-2, in No. 1 singles.
UCLA won its first national title since 2008. North Carolina was appearing in its first final.
McPhillips converted her fourth match point when Price's volley sailed deep, setting off the Bruins' celebration.
UCLA, which improved to 30-0 when winning the doubles point, also got a victory from Chanelle Van Nguyen in No. 4 singles.