Chris Tidland matched Watney's 64 to climb into second place at 12-under-par 201. Tim Wilkinson, the leader after Round 2, struggled to an even-par 71. He shares third place at 10-under-par 203 with D.J. Trahan (68), Bryce Molder (69) and Ryan Armour (69).
Watney got off to a quick start as he birdied each of his first two holes to move to minus-9. He kept going with a birdie on No. 5 and came back with a birdie on the seventh at Miccosukee Golf and Country Club.
The Fresno State alum picked up his fifth birdie on the front side at the ninth, which got him to minus-12. At the 10th, Watney faltered to his first bogey since his final hole in Round 1.
Watney atoned for the error with a birdie at the par-4 12th. The three-time All-American moved to 13 under with a birdie at the 14th. Watney dropped in an 8-foot birdie putt at the 16th and parred his last two holes to finish at 14under.
'I'm just trying to plod along,' Watney said. 'I'm trying not to do anything stupid. That has been big for me this week, giving away as few shots as possible.'
Watney entered the event 36th on the money list with the top-20 gaining their PGA Tour cards for next season.
'A win would be life-changing, but I can't go into tomorrow thinking about that,' said Watney. 'I'm happy to be in this position. This is why you play, to be in this position.'
Tidland moved into red figures with a birdie at the par-4 second. He ran off three straight birdies from the seventh to get to minus-9. The 32-year-old dropped in the fifth birdie putt of his round at the 11th.
The Oklahoma State graduate two-putted for birdie on 14 and came back with a 5-foot birdie putt at the next to move to 12 under. Tidland could not save par from a greenside bunker at 17, but stuck his second shot within 2 feet of the cup at the last for a closing birdie to tie his career low round of 64.
'I played really good today. My irons were the key,' Tidland said. 'You have to hit a ton of mid-irons on this golf course. I made some 20-footers today. I need to continue to putt well tomorrow to have a chance.'
D.A. Points, a two-time winner this season, posted a 3-under 68 to move to 9-under-par 204. He shares seventh place with Kelly Sellers (68) and Virginia Beach Open champion James Driscoll (70). Tony Carolan and Mathew Goggin are one stoke further back at minus-8.