Quinn, a redshirt, rallied to defeat Michigan's Ondrej Styler 6-7 (2), 7-6 (5), 6-2 to become the third Bulldog and fourth-ever freshman to win the men's singles crown.
Tian became the second Bruin to capture the women's title, with a 6-4, 6-2 win over Layne Sleeth, the first Oklahoma player to play in the final match.
Quinn, the first Georgia player to reach the championship since John Isner in 2007, faced four match points in the second set before taking control in the third to join two-time Georgia winners Mikael Pernfors (1984, 1985) and Matias Boeker (2001, 2002).
Quinn, from Fresno, California, closed the season with 17 straight wins and a 34-10 record.
Tian, from Beijing, China, didn't drop a set in six matches in Orlando, Florida, to finish the season with a 30-7 record. Keri Phebus of UCLA won the 1995 title.
In men's doubles, Andrew Lutschaunig and James Trotter of Ohio State defeated Cleeve Harper and Eliot Spizzirri of Texas 6-4, 6-4. It was the second doubles championship for the Buckeyes, the first coming in 2012.
The women's doubles championship was an all-North Carolina matchup as Fiona Crawley and Carson Tanguilig defeated teammates Reese Brantmeier and Elizabeth Scott 6-1, 2-6, 11-9. It was the third doubles crown in program history.
Last weekend North Carolina won its first women's team championship and Virginia defended its men's title.