Bryan and Gribble both teed off early at PGA National in Palm Beach Gardens, Florida, and produced six-under par 64s that none of the later starters could match.
But Gribble and Bryan, who is coming off a career-best tie for fourth at Riviera Country Club on Sunday, have no margin for error with Germany's Kaymer and India's Anirban Lahiri just a stroke back, with seven more players on 66.
Kaymer finished with back-to-back birdies for his 65, chipping in from the green-side rough at 17.
"It was just one of those shots you want to get within three feet or so," Kaymer said. "It was a bit of a bonus. You try to get away with a par and then chip in for two. I take it. Sometimes it works out the other way and you make a bogey."
Lahiri drained a 25-foot eagle putt at the 18th to join Kaymer at five-under.
Bryan and Gribble had set the target early.
Bryan played his first eight holes at even par before a birdie at 18, then poured in five birdies in his last nine holes.
He was happy to be back at PGA National, where he won his card for the Web.com Tour just over a year ago – going on to win three times on the developmental circuit to earn his PGA Tour card.
