Overton, who bested Alan Hill 2 and 1 in the second round Thursday morning, built a 4-up lead through five holes and cruised to victory against Kunick.
'In match play, you have to try to put a lot of pressure on the other guy so that he folds before you do,' said Overton, who has not trailed since the 12th hole of his first-round match. 'I went out and did that.'
Overton will take on Dayton Rose in the quarterfinal round as Rose moved on with a 1-up win over Nick Desai in the third round and a 3 and 2 victory over John Larson in the second round.
Brandt Snedeker outlasted 2002 champion Ryan Moore 4 and 3 in the morning session then went on to the quarters with a 3 and 2 win over Brendan Steele in the third round.
'I really tried to stay focused because it's easy to become complacent after you beat somebody like Ryan Moore,' said Snedeker, a first-team All-Amercian at Vanderbilt.
Snedeker has a date with Brady Stockton in the quarterfinals. Stockton needed extra holes in both of his matches Thursday as he took 20 hole to eliminate Roger Fine in the second round and 19 to defeat John Cassidy in the afternoon session.
Matthew Every beat Travis Johnson 2 and 1 in the second round then advanced to the quarterfinal round with a 4 and 2 win over Joe Kunz.
Every will battle Chris Stroud Friday morning. Stroud made it to the round of eight with a 4 and 3 victory over Jay Reynolds Thursday morning and a 4 and 2 win against Joey Stansberry in the afternoon's third round.
Timothy Kane, a 4 and 3 winner in the second round and a 5 and 4 victor over Danny Green in the third round, will take on Luke List in the quarterfinals. List romped Jeff Gilchrist 5 and 4 in the second round and edged out Jason Harris 1- up in the final third-round match Thursday.
The quarterfinal and semifinal rounds are on tap for Friday, while the 36-hole final is scheduled for Saturday.
The U.S. Amateur Public Links Championship, for bona fide public course players, is one of 13 national championships conducted annually by the United States Golf Association, 10 of which are strictly for amateurs.