Hoffman carded one-under-par 71, while Kisner fired a 68 to tie it up at 11-under 205 with one round left.
The two Americans have a three-shot lead over Englishmen Tyrrell Hatton and Matthew Fitzpatrick and Australian Marc Leishman.
World number three Rory McIlroy (65) soared to the edge of contention, the day's equal best score lifting the Northern Irishman within five shots of the lead.
Halfway leader Hoffman made a demoralising start with two straight bogeys, and further bogeys at the 14th and 15th holes left him in danger of falling off the leaderboard.
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"I knew I needed a good finish to run down Kisner," he told PGATour.com after turning his fortunes around with birdies at the final three holes.
He has birdied the par-four 18th all three rounds.
"Hopefully I don't need a birdie tomorrow but at least the feelings are good going into it," he said.
Co-leader Kisner said he had learned that protecting a lead rarely works against the best players in the world.
"I've learned these guys don't back up, so you've still got to make birdies and attack," said the 33-year-old from South Carolina, whose sole PGA Tour victory came late in 2015.
"There's no protecting leads out here, so I'm going to go play my game and make as many birdies as I can."
McIlroy is among those chasing the leaders on Sunday.
"I just played better, holed some putts," said the man who needs to win next month's Masters to complete the career grand slam of all four major championships.
"It's a score I was waiting on. I felt is was in there. It was just a matter of putting it all together and today I did. At least I've given myself a decent chance. I can take a lot from today."
This is the first staging of the event that carries his name since he died last September aged 87.
He was invariably at the 18th green to greet the leaders at the end of each round.
(Reporting by Andrew Both in Cary, North Carolina, editing by Gene Cherry)
