Rhea, an East Tennessee State golfer from Jonesborugh, lost 1-up to Zach Murray in the round of 64 match play portion of the tournament.
Rhea was 1 up through 12 holes when Murray made two birdies in a row to go ahead. Rhea won the 15th hole with par to get back to even.
Murray, an Australian, then made a birdie on the par-3 17th hole.
Rhea needed to win the famous par-five 18th to force extra holes and he made a birdie, but Murray also birdied the hole to clinch the match.