The reigning U.S. Open champion moved ahead of U.S. PGA Championship winner Vijay Singh on the final hole of the day after the Fijian world number one three-putted for a disappointing par five while Goosen made a birdie.
U.S. Masters winner Phil Mickelson also had a good 18th when his second eagle of the round completed a four-under-par 68, three shots off the lead.
British Open champion Todd Hamilton carded a two-under-par 70 to stand a further two shots back in the elite four-man $1 million event.
Goosen paved the way for his strong round with five birdies in the first six holes and he was happy to be ahead of the field with 18 holes to play.
"It was nice to get off to a good start, the greens were running well," he said.
"Phil had a good finish so he's back in the hunt but Vijay is the man to beat."
The highlight of Singh's round was an eagle three at the sixth, the Fijian hitting a five wood 240 yards and sinking the 15-foot putt.
"I just have to be patient. There's 18 holes remaining -- one shot, it's nothing," Singh added.
Mickelson played in his usual flamboyant style, but a series of poor putts will leave the Californian world number five disappointed not to have shot a lower score.
Hamilton struggled to make an impression after admitting he was not in top form earlier in the week and needs a major revival to overcome a five-shot deficit on Wednesday to claim the $400,000 first prize.