Knapp, who opened the tournament with a 59, started the third round on Saturday with a one-shot lead and was trailing by three shots when he made the turn. He holed a 12-foot birdie putt on the 16th and finished with a chip-and-putt birdie on the par-5 closing hole to stay in front.
"A little bit all over the place," said Knapp, who was at 16-under 197.
Right behind was fellow American Michael Kim — and nearly two dozen others.
There was so much movement in this captivating third round that 10 players had at least a share of the lead at one point. Some of them were undone by the 15th, playing 163 yards over water framed by a rock wall.
Taylor Montgomery, who had six birdies on the front nine and was the first player to reach 15 under, had a one-shot lead when he pumped two tee shots in the hazard on the 15th.
Swede Jesper Svensson, who earned a PGA Tour card through the European tour last year, was tied for the lead when he caught too much ball from a bunker behind the 15th green and it sailed into the water. He made triple bogey, and hit his drive into the water on the 18th. Tied for the lead with four to play, he wound up six behind.
Another victim was Kim, though he had fortune on this side. He had a one-shot lead going to the 15th when his tee shot caromed high off the rocks, veered hard to the right and was headed for the water when it landed softly in the muck.
Most of the golf ball was showing, so he removed his right shoe and sock and blasted out of the mud and onto the green about 25 feet away. He two-putted for his first bogey of the tournament.
"I didn't get as wet as I thought," he said, though his face had speckles of mud.
Russell Henley and Ben Griffin each had a 66, and Doug Ghim had a 68, to finish the crazy day just two shots behind, while Montgomery and Rickie Fowler (68) were three behind.
Twenty-two players were within five shots of the lead, a group that includes Jordan Spieth (68) and Brian Campbell (66), who won his first PGA Tour title last week in Mexico.
Knapp had the 15th score of 59 or lower on the PGA Tour, but only five of those other players went on to win. He will also will try to become the first wire-to-wire winner in tournament history.
"It just felt kind of weird after playing so well Thursday ... to hit shots and not have it be perfect every single time," Knapp said.
"Just had to manage my expectations and not get too frustrated about anything and just understand that it's a long week. There's plenty of great players out here who can go stupid low, so just have to try to stick to my game plan."
