The stocky Kokrak may need the added cushion as the chasing pack includes world number one Dustin Johnson, who shot his second 67 to be six-under on 134.
"All week I've been feeling better and better with the putter," said Kokrak. "Dave Stockton, Jr. and his dad have helped me out the last few weeks and things are starting to kind of go in an upturn."
Billy Horschel, the 2014 FedExCup champion, was alone in second on seven-under 133 after a 65, with Johnson joined at 134 by South Korean An Byeong-hun (66), Jhonattan Vegas of Venezuela (68) and Americans Cameron Tringale (68), Bud Cauley (67) and James Hahn (70).
Johnson, who won three tournaments in a row before withdrawing from last month's Masters after injuring his back in a fall before the opening round, said he is still working on regaining top form.
"Played a solid round," said Johnson, who gave a shot back with a bogey at his last hole. "I made a lot of good shots and rolled the putter pretty nicely."
Johnson said the back was no longer a concern.
"There's no issues there," he said. "Just need to keep practicing to get back. I had to take almost four weeks off, really didn't practice. It takes a little time to get back in the form I was in leading into the Masters. It's getting there."
The cut was set at two over par, with 76 players advancing to weekend play.
One notable absentee will be local favourite Jordan Spieth, who shot 75 for three-over 143, missing his second successive cut.
"Just disappointed," said Spieth. "I've got to figure out what I'm doing on the greens, first and foremost. I've got to get back into rhythm there. Short game is just off (but) it's close."
The world number six will be defending his title at Colonial next week.
(Reporting by Larry Fine in New York; Editing by Greg Stutchbury)
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