He posted an eight-under 205 total, while Canadian DeLaet carded a 68 to improve to seven-under, within sight of his first PGA Tour victory after going winless in 136 career starts.
Charley Hoffman and Ryan Moore trail by three shots, while Steve Stricker, the joint halfway leader, is part of a group sitting four behind.
Defending champion and world number one Jordan Spieth, who shot an opening 76, carded a 67 to sit equal ninth, six shots off the pace.
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Leader Haas, a six-times PGA Tour winner, has a chance to close in on the nine tour victories recorded by his father Jay.
"Everything I do in this game is because of what he taught me growing up," he told Golf Channel.
"Mentally, he’s usually that guy that puts things in perspective for me. If I’m complaining, he says if you want to have a long career, get used to the lows and just enjoy the highs.
"That’s kind of what I’m trying to do. It hasn’t been good lately but like this week shows, you never know what can happen, and hopefully I have a good day tomorrow."
Haas has also benefited from a putting tip from fellow pro Fowler, weakening his left hand to allow a purer stroke.
"It’s really helped me release the putter. It feels different," he said. "Right now it’s working."
DeLaet has three runner-up finishes on tour, along with three third-placings.
He is in contention again thanks in no small measure to an eagle at the par-five 14th, where he hit his second shot from 270 yards from the light rough to within three-feet of the pin.
"That was definitely the jump-start I needed," he said.
"I was up on this little perch and had a perfect look at the green. I hit three-wood basically as hard as I could."
Spieth, meanwhile, has not given up making a run at the leaders on Sunday.
"On this golf course, the leaders start getting four-to-five footers on greens that are a little inconsistent, who knows what’s going to happen," he told reporters.
"I really like the position we’re in. Obviously the lead would be better but we’ve got momentum on our side."
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford)
