Stewart Cink posted a 4-under-par 66. He shares third place with Tim Petrovic, Steve Flesch Jeff Maggert and John Senden.
Perks, a native of New Zealand, opened with a birdie on the par-5 11th after dropping his sand-wedge within a foot of the cup. He then ran off five straight pars at the Colonial Country Club.
'I got off to a great start. I hit a poor drive on 11, then hit a sand wedge real close,' said Perks. 'That kind of got me going. I did struggle with the driver a little bit, but hit some really, really good iron shots. And my short game was as good as it always has been.'
The 37-year-old rolled home a 15-foot birdie putt at the 17th and followed that up by chipping in for birdie at the next to head to the front side at minus-3.
Perks moved to 4 under after dropping a 9-iron within 8 feet of the cup at the par-4 third.
He birdied the par-4 sixth before another chip-in birdie at the seventh got him to minus-6. He parred the final two holes to cap a bogey-free round.
'I saw some good things last week, although the results really don't show it,' Perks said. 'I'm still really struggling with my driver, but I've been working hard. I think what paid off today, I didn't have to drive every hole. I hit a lot of 3-woods and 2-irons. I hit solid iron shots.'
Parnevik got off to a quick start with a two-putt birdie at the first and a 5-foot birdie putt on No. 2. He moved to 3 under as he dropped in a birdie at the fifth.
Parnevik, a five-time winner on tour, cruised to seven straight pars from there. At the 13th, he dropped a 7-iron within 10 feet and drained that birdie try.
The Swede tripped to a bogey at the next, however. He erased that mistake by rolling in a 20-foot birdie try on No. 15. Parnevik climbed into second place after dropping a wedge within 15 feet to setup his final birdie at the 17th.
'A great day. This is one of the courses I love to play every year, and I think the feeling is similar with most of the players on tour because it's a very old traditional style and it's not the grip it and rip it type of golf we play every week,' Parnevik said. 'I've been struggling pretty bad last year, and my No. 1 goal this year was to really make a strong effort to come back into the top 10 again.'
Defending champion Kenny Perry notched a 3-under-par 67. He shares eighth place with Chris Riley, Dennis Paulson, Carl Pettersson and Robert Allenby.
Olin Browne, the 1999 winner here, heads a group at 2-under-par 68. Among the notable players joining him there are Dallas-native Harrison Frazar, former Masters champion Mike Weir and five-time tour winner Stuart Appleby.