Quinney, a recent graduate of Arizona State, lost his last three holes of the day to Nosler after having led nearly the entire match over the East Lake Golf Club.
Two-down through 15 holes, Nosler took the 16th, following a rare Quinney-bogey, and then birdied the 17th from six-feet to square the match.
Nosler then made par at the closing par-3 18th, and watched as Quinney missed from five feet for the push.
Immediately following the match, Quinney promptly announced that he would turn pro.
'It was a fun year,' said Quinney, 'and it's going to be something I'm going to remember the rest of my life.'
For Nosler, he will now face Bubba Dickerson in the semifinals.
Dickerson, a junior at the University of Florida, beat Michael Sims 1-up in his match Friday.
In the other semifinal match, Robert Hamilton will face off against Manuel Merizalde of Columbia.
Merizalde destroyed Japans Taichiro Kiyota 6-and-5 Friday, while Hamilton beat Daniel Summerhays 4-and-3, and in the process, preserved a Tiger Woods-record, as Summerhays was gunning to become the youngest player ever to win the Amateur.
While Woods was 18 when he won his first of three titles, Summerhays was just 17-years-old.
Results from Friday's quarterfinals:
Robert Hamilton (141) def. Daniel Summerhays (142), 4 and 3.
Manuel Merizalde (142) def. Taichiro Kiyota (143), 6 and 5.
Brian Nosler (141) def. Jeff Quinney (142), 1 up.
Bubba Dickerson (141) def. Michael Sims (135), 1 up.
Saturday's Semifinal Matchups:
9:00 a.m. ' Robert Hamilton vs. Manuel Merizalde
9:15 a.m. ' Brian Nosler vs. Bubba Dickerson