The 38-year-old surged alongside overnight leader Colt Knost with the stunning run from the second hole and, though he dropped shots at the 11th and 15th, he birdied the last to complete a five-under-par 66 and nudge a shot ahead of his American rival.
Knost made an eye-catching bogey-eagle-bogey start as his playing partner pegged back his two-shot lead, but birdies at the fifth and ninth got him back on track.
A bogey at the 10th and a birdie at the 13th completed a two-under 69, leaving him one shot behind Pettersson's 13-under total.
Zach Johnson surged into third place with a 66 featuring an eagle at the long fifth. He gave one of those shots back at the seventh but four birdies on the back nine left him three off the lead.
Boo Weekley was on his own at seven under and defending champion Brandt Snedeker and Kevin Na each shot 69 to end the day six under alongside Robert Garrigus (70).
England's Brian Davis was five under after a 68, the same as Tommy Gainey, but compatriot Luke Donald could only manage a level-par 71 to stay two over as he struggles to defend his world number one ranking.
The Englishman needs to finish in the top eight at Harbour Town to remain ahead of Ryder Cup team-mate Rory McIlroy in the standings. He finished day three seven strokes off achieving that.
Sean O'Hair, who was in contention after three rounds at last week's Masters before fading, got his slump in a day earlier this time and props up the post-cut leaderboard on eight over after a 79.