Yip will face John Kelly in one of Saturday's semifinals as Kelly toppled Trip Kuehne, who lost to Tiger Woods in the 1994 final of this event, 3 and 2.
Webb Simpson defeated Alex Prugh, 2 and 1 to set up a semifinal match against Richie Ramsay. The Scotland native needed 21 holes to finally eliminate Rickie Fowler, 1-up.
On Friday, both the third round and quarterfinals were played since a long weather delay on Thursday pushed back play. The tournament is back on schedule with only the two semifinal matches scheduled for Saturday.
Yip flew out of the gate on Friday with wins on the first four holes. The first two victories came with pars, but Yip tallied birdies at three and four to go 4-up.
Fisher clawed back with a birdie and win at the fifth, then cut it to a 2-down deficit with a birdie at the ninth. Yip moved 3-up with a birdie at the par-5 11th, then the pair halved the next three holes.
At the par-five 15th, Yip got up and down from the rough for a birdie four. Fisher was in the back bunker in three and conceded Yip's birdie putt. Fisher also thought he was conceding the match, but after the miscommunication, he failed to hole out from the bunker, giving Yip the win.
'He's English, so I didn't really understand what he was saying. He just lost track of holes,' joked Yip. 'It's a great feeling and it's my greatest accomplishment in golf so far.'
Kelly jumped out on Kuehne with wins at one, three and six. Kuehne countered with a win at the par-5 seventh, and another at nine, both with pars to make the turn 1-down.
Kelly went 2-up with a par victory at 12, then closed out the match on 16 when Kuehne could do no better than a double-bogey.
'Obviously, he's a great player,' said Kelly, referring to his quarterfinal opponent. 'All I can do is play golf to the best of my ability. I can't do anything about who I'm playing.'
Simpson, like his fellow semifinalists, won early as he birdied the first to move 1-up. He won the fifth, seventh and ninth to make the turn a very comfortable, 4-up.
Prugh came back with birdies at 11 and 14 to cut the gap in half. When both players parred the par-3 17th, Simpson punched his ticket to the semifinals.
'This afternoon, I really drove it well,' said the Wake Forest student. 'I think I only missed a couple fairways, which out here is definitely the key. My first bogey was 16, so that was pretty good for match play.'
In the final match, Ramsay built a 3-up lead through 13 holes, but Fowler birdied the 14th and 16th hole and was conceded the 17th to square the match.
After a pair of halves, Ramsay birdied the third extra hole for the win.