Scheffler stormed from 14th overnight into third with 10 birdies – five on the front nine and five on the back.
He was denied a share of the lead only after a chip into a bunker on the par-four 14th led to a double bogey.
Scheffler shot 70 in the first round, which ended his run of 21 successive sub-70 scores, and 68 in the second.
“There’s definitely some tricks to this golf course, things you’ve got to get used to,” he said.
“There are things that are hard to notice in the practice rounds. But when you start playing under tournament conditions you start seeing a little of those nuances.”
US Open champion JJ Spaun and Russell Henley are best placed of the remaining eight Ryder Cup players on nine under.
Griffin, a captain’s pick who will make his debut at the Ryder Cup, said: “I’ve got to have that chasing mindset as a leader because I know all those guys behind me are going to stay aggressive and I’ve got to do everything I can to stay in front.”
