Couch, who played in the fourth group out on the course, is one stroke clear of the field at 12-under-par 204. Second-round leader Joe Durant birdied the last to card a 1-over 73 to join Charles Howell III (66) in second place at 11-under-par 205.
Two-time Masters champion Phil Mickelson carded a 4-under 68 Saturday to move into a tie for sixth place at 9-under-par 207.
Couch got going with a 25-foot birdie putt on the third. He rolled in a birdie effort from off the green at the fifth, then got up and down for birdie on the par-5 sixth to move to 7 under.
The Florida-native birdied the par-3 eighth. Couch's approach at the ninth stopped inside 15 feet and he drained that for the fifth birdie of his round.
Couch, a five-time winner on the Nationwide Tour who is going for his first PGA TOUR title, poured in a 12-footer for birdie on 11 and capped a run of four in a row with an up-and-down birdie on the par-5 11th. Couch carded three straight pars to remain at 11 under.
He two-putted for birdie on the par-5 15th. Couch, who will turn 33-years- old on Monday, sank a birdie on the par-3 17th to move to 13 under par. However, he dropped a shot at the last to finish at minus-12.
'It was blowing from the get-go,' said Couch of the wind. 'I think it blew hard all day. It was very tough all day. I hit it really good and made some putts today. I had one bad shot there on 18, but other than that I played solid.'
Howell flew up the leaderboard with a hot front nine. He birdied each of the first two holes to move to 7 under and birdied three of the last four holes on the front nine to turn at minus-10.
The 26-year-old posted his sixth birdie on the par-5 11th. Howell, whose lone TOUR win was at the 2002 Michelob Championship at Kingsmill, came back with a birdie on the 14th. He faltered to a bogey at the last though to end one back.
'When I woke up this morning and saw the wind in the forecast, I was worried because this golf course is not easy in wind like this,' Howell stated. 'It really helped seeing Couch play good early. I see low numbers out there and think there is something out there for me.'
Durant was up and down all day. He bogeyed No. 1, birdied the next, then dropped another stroke on the third to fall to 11 under, one behind Couch.
The 42-year-old fell two behind Couch as he bogeyed the fifth. Durant got that stroke back with a birdie at the par-4 seventh. He struggled to three consecutive bogeys from the ninth to tumble to minus-8.
All looked lost for Durant, but he flew right back up the leaderboard with three straight birdies from No. 11 to get back in it at minus-11.
The three-time PGA TOUR winner had a short approach to the par-5 15th, but dumped that in the water. Durant managed to save bogey, but that dropped him to minus-10. He poured in a birdie putt from just inside 26 feet at the last to get back within one stroke of the lead.
'The wind blew the same direction all day, but it was very gusty, extremely gusty at times and it made choosing clubs almost impossible,' Durant admitted. 'The only thing I could really do today was keep my patience. I knew it was going to be difficult.'
Mickelson was joined at minus-9 by Stephen Leaney, Ian Poulter, Brett Wetterich, two-time winner here Carlos Franco, Matt Hansen and Tim Herron.
Louisiana-native and 2001 champion David Toms is one stroke further back at minus-8. He was joined there by seven other players.