Bemowski was a 3 and 2 winner over Jack Forbes in the second round. He then ousted Spencer Sappington 1-up in 19 holes. Bemowski will face Greg Reynolds in the quarterfinals.
Reynolds, the 2002 winner, birdied the 18th and 20th holes to take his third- round match, 1-up over Ronald Vannelli. The winner of the Bemowski-Reynolds match will take on Alan Foster or Robert Mielcarz in the semifinals.
Foster cruised to a pair of big wins on Tuesday. He claimed each of his matches by a similar 6 and 5 score.
Jack Vardaman will face Randy Reifers in the third quarterfinal match. Vardaman took down Stan Fischer 3 and 2 in the third round.
'I've lost in extra holes twice in the quarterfinals,' said Fischer, who after his second-round win. 'I want to win again so I can get an exemption for next year.'
Earlier in the day, Fischer ousted stroke-play medalist Billy Clagett, 3 and 1.
'I don't know where it went, but it went,' said Clagett of his previous strong play. 'He didn't play like an amateur, but I did.'
The winner of that match will take on Mike Rice or Gayle Sanchez in the other semifinal match.