"There's no advantage. He wants to win. I want to win," said Watson, a two-time PGA Tour champion but winless in the previous three events he has had at least a share of the third-round lead.
"There's always pressure you put on yourself and then the outside pressure that everybody else seems to put on you. You have to get used to that. So for him not winning his first one might be a little tougher for him, but I'm just as nervous as he is. I might have a half a percentage better chance than he does."
Watson made a 4-foot birdie putt on the par-5 18th hole for a 2-under 70 and a share of the lead.
Simpson, seeking his first tour title, birdied Nos. 3-7, then closed with 11 pars for a 67 to match Watson, who has had at least a share of the lead after all three rounds, at 12-under 204 at TPC Louisiana.
Watson needed to birdie the 588-yard 18th to get into the final group Sunday. After hitting his 250-yard approach into a greenside bunker, he blasted out to 4 feet to set up his birdie putt.
"Knowing that if I stroke this well, I'm tied for the lead and not one back, knowing I'm in the final group," said Watson, the Torrey Pines winner in January. "There was a lot of pressure on that for me. Somehow it went in dead center, and so I'm in the final group."
John Rollins (69) was third at 11 under, and 2002 winner K.J. Choi (67) was 10 under along with Steve Stricker (68), George McNeill (65), Charles Howell III (66), Tommy Gainey (68) and Matt Jones (69). Former LSU star David Toms, the 2001 Zurich winner, topped a group at 8 under after a 67.
Simpson has a share of the 54-hole lead for the first time in his career.
"I've always slept pretty good going back to college and amateur days holding the lead," said Simpson, who tied for second behind Phil Mickelson on April 3 in Houston. "But this is why we do what we do. This is why we work out, why we practice, to give ourselves a chance to win on the PGA Tour.
"I think that will kind of calm my nerves."
Rollins is a three-time tour winner. "I've felt very comfortable on the golf course this week," Rollins said. "We've got three good ones, hoping for one more."
Watson made a 3-foot birdie putt on the first hole to open a two-shot lead. He appeared to be in position to increase the lead on the par-5 second after a 321-yard drive, but his 3-iron approach from 256 yards rolled over the green and came to rest near a cypress tree. He stubbed his chip and settled for par.
He three-putted the par-3 third hole for bogey from 47 feet and added another bogey on the sixth to fall back to 9 under, at that point two shots behind Simpson, who was playing three groups in front of Watson.
The 32-year-old Watson then birdied the two par-5s on the back nine to tie Simpson.
"It was hard to make a lot of putts, for me," Watson said. "The greens are getting burned out. Hopefully, they don't lose them by Monday. Some of them are getting pretty brown.
"Other guys on the board were making some putts, but for me it was a tough day."
Simpson quickly made up a three-shot deficit, beginning with a 6-foot birdie putt on the third hole. He followed with a 33-footer on the fourth and a 16-footer on the fifth hole to get to 10 under.
A 62-foot chip-in on the sixth gave him the lead at 11 under, and he closed out the streak with a 4-footer on the par-5 seventh hole.
"It just kickstarted the round for me," Simpson said. "I've been playing well I feel like as of late. Today was a little more exciting. "
Simpson brought some unwanted excitement to his final hole when his second shot flirted with the water. He chipped up and two-putted, happy to escape with par.
"I thought it was in the middle of the lake but somehow it stayed left," he said. "Just a poor swing. It was a good break there."