Watson, the 2010 winner of the event, shot a three-under 67 to move to 10-under 130, two shots clear of Ireland's triple Major champion Padraig Harrington (66) and US Tour rookie Patrick Reed (66).
Australian Nick O'Hern (66) was in a share of fourth place with Americans Hunter Mahan (71), Tommy Gainey (67) and Tag Ridings (65) at seven-under.
Watson backed up his opening-round 63 with four birdies and a bogey and despite taking a solid advantage into the weekend claimed his game was a little off.
"It was a struggle and I just had to play it in safe," the former Masters champion said.
"I just didn't feel it today, body, whatever it is, you know waking up early I just didn't feel 100 percent so I just hung it together, just tried to play to the fat of the greens, play smart and try to take all the trouble out of play."
Overnight leader Charley Hoffman was four shots off the pace after a three-over 73 that included a double-bogey, three bogeys and two birdies.
Harrington carded a second successive 66 but was not exactly flush with confidence despite being well placed going into the final two rounds.
"I'm not buzzing with confidence out there," Harrington said.
"I'm very pleased with the score but my score is flattering, given how I played a little bit, I holed some long putts out there so I feel like I need to play a bit better on the weekend. I can't always rely on holing 20-25 footers."
Major winners Keegan Bradley (65) and Webb Simpson (69) sit just four shots off the pace while last week's US Open winner Justin Rose (68) was a further shot back at five-under.
With Zach Johnson also five back, six Major champions sit inside the top 12 of a neatly stacked leaderboard.
"Getting up this morning was a tough one, the night was very, very short," Rose said. "Tomorrow is an important day to just keep the momentum going, keep the adrenaline going for Sunday and try to make something happen."
Among those to miss the cut were former US Open winner Lucas Glover, former Masters champions Mike Weir and Trevor Immelman, Belgian Ryder Cup player Nicolas Colsaerts and former Ryder Cup captain Davis Love III.
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- Padraig Harrington
- Tommy Gainey