Kelly is at 10-under 134 after 36 holes at the TPC-Louisiana course, one shot better than Troy Matteson (64) and Charley Hoffman (66).
Louisiana native David Toms (68) moved into a tie for fourth place with Parker McLachlin (69), John Merrick (69), John Rollins (67) and first-round leader Charlie Wi (70).
Kelly, whose only two tour triumphs came in 2002 at the Sony Open in Hawaii and the Western Open, birdied seven holes to equal his lowest score of the year. His best finish to date in 2009 came in Cancun, Mexico, in a tournament played the same week as the WGC Match Play Championship.
"I'm coming off just a bad few years it seems like," Kelly said. "I haven't really had that kind of comfort factor. It was just really comfortable out there the last couple of days."
For the second straight day, Masters runner-up Kenny Perry let a good round slip away over the closing holes. Perry bogeyed the final two holes in the final round at the Augusta National and lost in a playoff to Angel Cabrera.
On Thursday, he suffered two bogeys in the final four holes en route to a 3-under 69. On Friday, he finished bogey, double bogey for a 70. He was tied for 21st place at 139.
Swim Week Miami Beach 2014 [PHOTOS]