Australian Stuart Appleby is in third place by himself at 14-under-par 202 after a third-round 66. Trevor Immelman is one shot behind him at minus-13.
Couples, who was one of three players to share the lead after round two, made a late charge to grab the lead. On the front side, he carded three birdies but also had a bogey and a double bogey.
The 1992 Masters champion birdied the first before three-putting for bogey the third. He recovered that stroke with an eight-foot birdie putt at the par-4 fourth.
After a pair of pars, Couples double bogeyed the par-4 seventh after his second shot found water. He got one of those strokes back with a birdie at the ninth.
'A big part of the round was I hit it in the water on seven and then I hit a beautiful iron to the eighth hole,' said Couples. 'I missed the putt on eight and was screaming at myself all the way to the next tee. I wanted to be more aggressive.'
On the back nine, Couples ran off four straight birdies from the par-5 12th to move into a share of the lead with Calcavecchia at minus-15. The longest putt during that run was from 12 feet and Couples sank a 10-footer for birdie at the last hole to take over first place.
'I played great the back nine,' said Couples. 'It has been a long time since I've been in this position. If I go out and play well, I should be fine. I just have to do what I did today.'
Couples, a University of Houston graduate, is trying to become the first Houston alum to win the hometown event. He has led 19 times entering the final round on tour and has won eight of those tournaments. However the last four winners and nine of the previous 15 on the PGA Tour this season have been come-from-behind victors. .
'Tomorrow is going to be a slugfest, or a puttfest, whichever way you want to look at it,' said Couples, whose last win came at the 1998 Memorial. 'I can't worry about being in the lead or what is going on out there. But I know there is going to be a slew of birdies out there and I just hope to go out and play well.'
Calcavecchia had two birdies and a bogey on the front side. He made back-to- back birdies from the 12th to get to minus-14 and he birdied the 15th just before Couples to briefly hold the lead by himself. At the last two holes, Calcavecchia was unable to convert birdie opportunities.
'Playing with Fred tomorrow should be fun. We've played a lot of golf together, including a couple of Ryder Cups,' said Calcavecchia. 'I will definitely look at the scoreboard tomorrow. I like to know what is going on out there.'
Appleby, who has gone 27 holes without a bogey, rolled in a 20-footer for birdie at the first. He later drained a 15-foot birdie at the par-4 sixth. The Aussie stuck a 5-iron within three feet at the eighth to setup another birdie.
On the back side, Appleby carded back-to-back birdies from the 11th. He climbed into third place with a two-putt birdie at the par-5 15th.
'I had a long streak of bogey-free golf at the Masters, but I didn't really do that well there,' said Appleby, who went 50 holes without a bogey at Augusta. 'I'd have to say around here, you don't want to make too many bogeys, but you certainly need to make three times as many birdies.'
Hank Kuehne, who shared the lead with Couples and Calcavecchia after Friday's second round, shot an even-par 72 and is tied for ninth at 11-under-par 205. Defending champion Vijay Singh is tied with Kuehne among a group of six players tied for ninth five shots behind Couples.