Watson was one of 27 players who returned to the Tournament Course at Redstone at sunrise to complete his suspended third round. Thunderstorms delayed tee times for six hours on Saturday.
Watson's 64 tied the course record set by Johnson Wagner on Saturday.
Wagner, a 27-year-old Tour rookie, was part of a five-way tie at 11 under, along with defending champion Stuart Appleby, Houston resident Jeff Maggert, Adam Scott and Paul Stankowski.
Watson had three holes to play on Sunday morning and birdied the par-3 16th to move to 16 under. He missed the greens on nos. 17 and 18 and bogeyed both to finish the round at 14 under.
Appleby, playing with Watson, birdied the 17th and finished with a 67. It was the Australian's sixth sub-70 round in seven at the Redstone course, which debuted as the tournament host last year.
Maggert also shot a 67 after a bogey on the 18th. Scott and Stankowski completed their third rounds, both 65s, on Saturday, just before play was halted due to darkness.
The final round was scheduled to begin at 11 a.m. ET, with threesomes teeing off both No. 1 and No. 10.
Stankowski just regained his PGA Tour card last year after finishing eighth in qualifying school. He shot his best round of this year on Saturday after missing three cuts in his first five starts.
Stankowski is just happy to be playing at all. He's endured three surgeries -- two on his left hand and another on his shoulder -- in the last three years.
For a while, he couldn't even pick up a club, let alone swing one.
'I'm thankful for just the opportunity to be able to put the peg in the ground and come out here,' said Stankowski, winless since the 1997 Hawaiian Open. 'Being in contention, having a chance (Sunday), that's just icing on the cake.'
Wagner started the third round at 3 under, three shots behind a six-way tie at the top. He teed off almost two hours before the leaders and made the most of the ideal scoring conditions after the storms.
He reeled off five straight birdies, including a curling 25-footer on No. 6, to finish a front-nine 30, then added two birdies on the back to beat Greg Owen's 65 in the second round of last year's Houston Open.
'It was an incredible run,' Wagner said. 'I kind of got in a zone.'
The Amarillo native finished second on the Nationwide money list in 2006 to earn a PGA Tour card. He's discovering quickly how much more difficult it is to win at the top level.
Wagner has shot at least one round in the 60s in seven of nine starts this year. But his final-round average is 73.5, including an 80 at the Honda Classic and a 76 in Tampa the following week.
'I just have not been able to get a good Sunday round,' Wagner said. 'I'm learning a lot out here. Hopefully, my experiences will help me this weekend.'
Wagner came into the tournament ranked sixth in greens in regulation. He hit 16 of 18 on Saturday and needed only 26 putts, four of them from beyond 14 feet.
If only he can keep his touch for one more day.
'Going into the past few Sundays, I've always been five or six back and feel like I've had to press early,' he said. 'I know now I have a really good chance to win. I'm going to be real patient and not try to press from the beginning.'
Watson leads the tour in driving distance and used his power to shred the fifth-longest course on tour. He birdied all four par 5s after hitting 300-yard drives.
Scott, the highest-ranked player in the field at No. 5, missed several short putts on Friday and shot a 71. He holed a 23-footer on the No. 6, capping a stretch of four straight birdies.