Haas was 3-down at the turn but climbed back into his match. He won the 10th and 12th holes with birdies and drew even when Trahan bogeyed No. 15.
Haas captured the lead with a par at the 16th hole and when Trahan missed a long birdie putt at the 17th, Haas was there to capitalize. Haas drained a 10- footer for birdie at 17 to close out the match.
'I was shaky from the start,' said Haas. 'But I think when I get over par, or down in a situation, I tell myself I'm not a 75 shooter or a 74 shooter. I tell myself I'm a 70 shooter and it evens out.'
'[Bill] was in play all day,' said Trahan, winner of the Amateur Public Links title in 2000. 'I don't know how many fairways he missed, but it wasn't many.'
The third round was not as kind to another son of a PGA Tour veteran. Kevin Stadler, the son of 1982 Masters champion Craig Stadler, was bested by John Klauk 1-up when Klauk won the final two holes for the victory.
Stadler took a 1-up lead at the 16th hole when he chipped in from 36 yards. Klauk squared the match with a birdie at 17 and when Stadler missed a six-foot par save at 18 and Klauk ran home a five-footer, Klauk was the victor.
'We were just all over the place today,' said Klauk, who won the Western Amateur earlier this month. 'Both of us, we just hit a lot of shots that were all over the place.'
'It was pathetic,' said Stadler. 'It was the worst round of golf I think I played in I don't know how long.'
Haas will take on Klauk in Friday's first quarterfinal match.
Spencer Levin, an 18-year-old from California, advanced to the quarterfinals with a 4 & 3 win over Brad Morris.
Levin will face Ricky Barnes in the quarterfinals after Barnes posted a 2 & 1 victory against Brett Foulds.
Ryan Moore continued his dominance Thursday with a resounding 5 & 4 win over Bruce McDonald. In Thursday morning's second round, Moore clobbered David Miller 7 & 5.
'It's feeling pretty similar right now,' said Moore, after his victory over McDonald. 'I think I definitely carried that confidence [from the morning round] with me.'
Moore's quarterfinal opponent will be Dustin Bray, who moved on with a 3 & 2 victory against Camilo Villegas. Moore and Bray will battle in Friday's final quarterfinal match.
The two remaining matches from Thursday went down to the 18th hole.
Hunter Mahan, the 1999 U.S. Junior Amateur champion, held on for a 1-up victory over Conner Robbins. He will face 2001 U.S. Junior Amateur champion Henry Liaw, who beat Seth Porter 1-up in the third round at Oakland Hills.
Mahan built a 2-up lead after 16 holes and hung on despite losing the 17th when he bogeyed the hole.
Liaw, 16, birdied the 16th hole to go 1-up and drained a curving par save at the 18th to avoid extra holes and win the match.
'Since I'm at the quarters, I can't just settle here,' said Liaw. 'I've got to keep playing and see what happens.'