Anirban Lahiri of India joined Kaymer at 65 by rolling in a 24-foot putt for eagle on the par-five 18th.
Kaymer caught fire after hitting his tee shot into an awkward lie in rough on the edge of the par-three 17th green.
"It was just one of those shots you want to get within three feet or so," two-times major winner Kaymer told Golf Channel.
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"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."
Gribble has already won this season, taking the Sanderson Farms Championship, while Bryan contended last week at the Genesis Open before finishing tied for fourth in his 13th PGA Tour start.
Bryan feels at home at PGA National, where he won his Web.com card at Q-School 14 months ago and went on to win three times on the tour to automatically graduate to the PGA Tour.
"A place that I’m comfortable at, and a golf course I know, they are few and far between out here,” Wesley said about PGA National. "It’s my first run at all these tournaments out here. I love this place, love this golf course and I had a great day.”
Seven players were tied two shots back in the opening event of the Florida swing that begins the run towards the first major of the year, the Masters.
Knotted at 66 were Americans Rickie Fowler, Ben Crane, Sean O'Hair and Ryan Palmer, along with Briton Ian Poulter, Canadian Graeme DeLaet and C.T. Pan of Taiwan.
Defending champion Adam Scott of Australia and last year's runner-up Sergio Garcia of Spain were another two strokes adrift after opening with 68s.
(Reporting by Larry Fine in New York; Editing by Frank Pingue)
