Eaton's semifinal opponent on Saturday will be Italy's Edoardo Molinari, who squashed South Africa's Dawie Van der Walt, 6 and 4.
The other semifinal match will feature Dillon Dougherty against Canada's J.C. Deacon. Dougherty dispatched Canadian Ryan Yip, 4 and 2, while Deacon eliminated fellow Canadian, Mark Leon, 2 and 1.
Eaton went 2-up with birdies at the first two holes, but by the 10th hole, the match was all square. Eaton won the 11th with par, then took the 13th, 15th and 16th holes with pars.
That was enough to knock out Kim.
'My experience helped me quite a bit,' said Eaton. 'I felt very comfortable. I knew if I stayed within myself and made good swings I'd be fine. I've been there before. I have a USGA championship so I am not going to press to get another one.'
Molinari took the lead for good with a birdie at the third. He went 2-up around the turn, then won 10, 12, 13 and 14, three with birdies, to easily move into the semifinals.
Dougherty was only 1-up after losing the 12th hole, but extended his lead to 2-up with a birdie at No. 13. He parred 15, then birdied 16 to close out the match.
Deacon won the third with a bogey, then built his margin to 3-up at the ninth. Leon capitalized a pair of bogeys at 10 and 12, but Deacon rolled in a 35-footer for birdie at the 14th to move 2-up.
The duo halved the next three holes to propel Deacon into the round of four.
'He made that bomb on 14 and then he had the momentum,' said Leon. 'He made ups and downs. He was so clutch all week.'
The semifinals are Saturday morning, then the 36-hole final is on Sunday.