The American pair moved into 20 under overall after a fine day in the four-ball format at TPC Louisiana, where teams were greeted with walk-up music for the first time on the PGA Tour.
Kisner and Brown holed 10 birdies and two bogeys during the third round to edge into a one-shot lead.
Tony Finau and Daniel Summerhays fired a nine-under 63 to be in a tie for second with second-round leaders Michael Kim and Andrew Putnam (66).
But with the tournament finishing with the foursomes format, it remains wide open heading into the final round.
Brice Garnett and Chesson Hadley are in outright fourth at 18 under after shooting 11-under 61 on Saturday.
That was the round of the day and managed by three teams, including Billy Horschel and Scott Piercy, as well as Jason Dufner and Pat Perez.
Those duos are a shot further back at 17 under and still well in contention.
Justin Rose and Henrik Stenson remain in the hunt, but a 65 left them at 15 under and tied for 14th.
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