The two-time European Tour Order of Merit winner's round featured five birdies and a bogey on the 18th as he led the way by a stroke from America's Justin Leonard, who also posted a four under 66.
"I got off to a nice start and played pretty solid," said Goosen. "I'm happy with the round. I've not done so well around this course in the past, so it's nice to play well for two rounds and see how I can do on the weekend."
Goosen went out in a one under 34 before registering three birdies on the way in, although he dropped a shot at the last for a second day running.
"The last hole, I hit a good drive and just had an eight iron to the green and pulled it and then hit a poor chip and a good putt that didn't go in," he added.
"I think the turnaround was on the fourth. I hit a good drive down the fairway and had a lot of mud on the ball and hit a six iron that went probably 25 yards left of the green, and I chipped it in.
"So that was sort of the turnaround. You're looking at definitely maybe making bogey there and chipping it in there sort of turned my round around and kept it going."
Overnight leader Bubba Watson was at even par through five holes of his second round as he kept himself well in contention.
Phil Mickelson's two early birdies moved him into a share of fourth place alongside Sweden's Peter Hanson, who shot a four under 66, and America's Bo Van Pelt, who shot 68 to follow his three under par first day effort.
Australia's Adam Scott, England's Paul Casey, Miguel Angel Jiménez of Spain, American Nick Watney and last year's US Open Championship winner Lucas Glover were all back in the clubhouse and tied for seventh place after moving to four under overall.