Villegas added a bogey on the 13th, didn't make a birdie on the back nine and had to settle for a 70.
The layout didn t feature when Streb won his only prior US PGA Tour title at Sea Island in 2015, but the American looked right at home as Thursday s blustery winds gave way to balmy weather.
After opening with a 64, the former world No 7 made a 12-footer for eagle on the 18th at the Plantation Course for a six-under 66 that left him on 12-under par, two shots behind Robert Streb who fired a career-low, nine-under 63.
It was in 2014 when Streb closed with a 63 to make up a five-shot deficit before winning a three-man playoff. He lives at Sea Island, and no resident has ever won this event.
Burgoon made five birdies in six holes on the back nine and matched Streb's 67 to stay three behind alongside Johnson, while Emiliano Grillo raced to 13 under when he got hot with the putter over the last four holes.
Burgoon had five birdies in a six-hole stretch on the back nine - the exception was a bogey on the 14th, playing straight into a strong wind along the water - to overcome a rough start and get into the final group.
Four-time PGA Tour victor Villegas hit a daring approach shot on his final hole and then coolly converted an eagle putt to follow up his opening round 64 with a solid 66.
Streb began his round with a quick hook and escaped trouble with par.
It never felt easy, but he wasn't losing any ground.
LPGA: Sei Young Kim answered Ally McDonald's ace with a late birdie run to open a five-stroke lead in the Pelican Women's Championship in Belleair, Florida.
Tenth-ranked Tyrell Hatton of England holed his second shot from 110 yards for an eagle on the 16th hole in a 69 and is tied for 31st, while sixth-ranked Webb Simpson, who has lost twice in playoffs at the RSM including past year, is tied for 41st after a 66. 14-17, to get to 14-under 196.
"It was playing like 115 front, 127 hole, and there was a little bit of downwind", McDonald said.
"I pushed my drive, it bounced on the cart path", he said.
"(I m) just trying to finish as well as I can and see if I can get in a better spot for the spring", he said.
"We ve only played 36 holes", Villegas said. "I m not going to say the confidence is coming back from these two past days, but I think having the shoulder good and all the work that I ve put in the last few months made me feel better".