B.J. Staten fired a 7-under 64 in round three and is alone in second place at minus-16.
Ron Whittaker (63), Jason Day (62), Kelly Grunewald (65) and Scott Sterling (69) are knotted in third place at 15-under-par 198.
Thatcher began the third round with a two-shot lead and played steady golf. While this tournament is notoriously a shootout, Thatcher stayed atop the leaderboard with solid pars.
He did not collect his first birdie until the par-4 fifth hole. Thatcher parred his next six holes, but got his round going early in his second nine.
At the par-3 12th, Thatcher knocked his tee ball to 12 feet. He holed the birdie putt and made another birdie putt from a similar length at the very next hole.
Thatcher continued his par run, but appeared to be in a little bit of trouble at the closing hole. His pitching wedge approach spun back to 30 feet and after a poor birdie effort, found himself with five feet to save par. Thatcher converted the par putt to take a two-shot lead into Sunday.
'Not giving up a lot of shots is a key,' acknowledged Thatcher. 'It's a good position to be in. I'm happy to be here, but I'm definitely a little disappointed in how I played some of the easier holes.'
Thatcher's disappointment was rooted in the fact that he parred all three par 5s on Saturday. He also did not take advantage of two driveable par fours on the front.
'I went out and parred all three par 5s and the two driveable par 4s,' said Thatcher. 'That's the difference between me having a really comfortable lead today and playing a really good round tomorrow.'
Brad Adamonis (63), Jason Enloe (66), Martin Laird (66), Michael Long (66) and Miguel Carballo (68) are tied for seventh place at minus-14.