With one round to play, Pettersson leads on 12-under-par 201 after overturning an overnight two-stroke deficit on Knost, who slipped back with a 69.
The fast-starting Pettersson started his birdie streak on the second hole under sunny skies at Hilton Head Island, South Carolina.
"I didn't know how many I had made in a row," the four-time US Tour winner said. "I was in my own little world for a while."
Bogeys on the 11th and 15th holes halted his charge but the Swede concluded his round with a birdie on 18, his seventh of the day.
He and Knost will be paired together again on Sunday.
"It is always tough playing with the lead," Pettersson said, “but I look forward to the challenge."
Knost started the third round badly, knocking his opening tee shot into the trees and wound up with a bogey on two of his first three holes.
The American sandwiched an eagle between the misfires, rolling in a 48-footer from just off the green of the par five second hole.
Knost also bogeyed the third and 10th holes and ended the round with three bogeys, three birdies and his eagle.
Former Masters champion Zach Johnson equalled Pettersson's low round of 66 to move within four strokes of the lead heading into Sunday's final round, one ahead of two-time Heritage winner Boo Weekley.
Briton Luke Donald's grip on the number one ranking loosened further after an even par 72 left him 14 shots off the lead and seven away from a top eight finish that would ensure he remained ahead of Northern Irishman Rory McIlroy in the rankings.