The German, who says his mind is uncluttered after all but quitting social media, signed for a 15-under 201 total with one round left.
Scott, a fellow former number one, also continued a recent resurgence, the Australian matching Kaymer's 66.
Japan's Hideki Matsuyama had the day's best score, chipping in for birdie from lush rough at the last for a 64 that lifted him within four strokes of Kaymer.
Americans Jordan Spieth (69) and Patrick Cantlay (68) are also four behind.
Kaymer had a wrist injury that set him back 18 months ago, but he said his recent poor form had been caused more by his state of mind than due to any physical ailments.
"I think social media and listening to a lot of the broadcasting and stuff can take a lot of energy and for me it's more distracting than helping," he told CBS television.
"It takes a lot of energy to read that stuff, even if it's not about yourself. You think about other people and then automatically compare yourself and once you compare yourself you limit yourself."
Second-placed Scott ended his day in style at the 18th with a brilliant eight-iron approach before using his long putter to brush in the three-foot birdie for a round of 66.
The 2013 Masters champion said he would be delighted to replicate Saturday's form on Sunday.
"I would almost take that same round tomorrow with below average putting and see how my chances stack up but I'm going to need a really great round," he said of his chances of overtaking Kaymer.
Scott has won 14 times on the PGA Tour, but not since 2016.
His recent form has been solid, including a top-10 finish at the PGA Championship two weeks ago.
(Reporting by Andrew Both in Cary, North Carolina, editing by Pritha Sarkar)
