The second-seeded Giron (30-5) is the UCLA's first singles champion since Benjamin Kohlloeffel in 2006.
Sarkissian (34-10) was attempting to win the Waves' second NCAA title and first since 1988.
In the women's final, Danielle Collins of Virginia beat California's Lynn Chi, 6-2, 7-5, to become the Cavaliers' first national singles champion.
UCLA Coach Billy Martin, who won a national singles title for the Bruins in 1975, called Giron “the hardest-working kid” he's had in 21 years overseeing the program.
Giron won after UCLA teammate Clay Thompson, the tournament's No. 1 seed, was upset in the first round by South Florida's Roberto Cid. Sarkissian beat Cid in the quarterfinals.
Giron's victory gives him an inside track to earn a spot in the main draw of the U.S. Open.
Collins, Virginia's first woman to advance as far as the national quarterfinals, won 11 straight points in the second set to rally from a 3-5 deficit.
After relying on her backhand earlier in the match, Collins (36-10) switched strategies and was able to choose easy targets with her forehand.
Collins also took advantage of Chi's second serve most of the afternoon.
“I never thought that I'd get to the finals,” Collins said. “It's unbelievable. I never expected that or anything near that.”
Chi (38-11) was trying to become the Bears' second singles champion in four years. Alabama won its first doubles title, as the fourth-seeded tandem of Maya Jansen and Erin Routliffe beat Georgia's No. 2 team of Lauren Herring and Maho Kowase, 6-1, 6-0.