This event features golf's four professional major champions in a 36-hole stroke-play tournament.
Goosen distanced himself from the group at the par-5 sixth when he roped a 3-wood from 255 yards out, but missed the green long. He holed a sand wedge from 25 yards for an eagle-three to reach 5-under-par.
'I had a pretty good lie down in the rough and it was a good chip shot, just ran it perfect and it landed and went in the hole,' said Goosen, referring to his eagle. 'That was nice.'
Goosen broke out quickly at Poipu Bay Resort Golf Course with a four-foot birdie putt at the par-5 second. He added a six-footer a hole later after he hit a beautiful tee shot at the 203-yard par-3.
The U.S. Open champion wedged his approach inside five feet at No. 5 to set up his third birdie before the eagle at No. 6.
Goosen would like to cap off his best career season. The 11-year veteran won his first major at Southern Hills in June and became the first non-European to capture the Order of Merit title (leading money winner) since Greg Norman in 1982. He is also playing well coming into the Grand Slam after teaming with Ernie Els to win the WGC-EMC World Cup of Golf last weekend.
'I'm pretty confident and happy with the year,' said Goosen, who added a five-foot birdie at No. 14. 'I was just trying to get a little bit comfortable on the tee. I kept in play today so that was the main thing.'
Woods also got off to a hot start with birdies at his opening two holes. He added a tap-in birdie at No. 6 which was amazing considering he drove behind a tree but hooked a 6-iron to six feet. He missed the eagle try but tapped in for birdie.
The three-time defending champion nailed a pitching wedge to nine feet at No. 7 to reach 4-under par, but dropped his first shot of the round at No. 9 when missed the green with a sand wedge and failed to save par from 16 feet.
Woods rebounded with five-foot birdie at the 10th and parred the next seven holes. He two-putted from 45 feet at the last to get within one of Goosen.
'I was very happy to shoot what I shot today because I was not driving the golf ball the way I wanted,' said Woods, the only player to win this event three times in a row. 'To end up at 5-under par, I was pretty happy with that.'
Toms went on to the back nine tied with Goosen at 5-under. He birdied two of his first four before he made three birdies in a row, starting at No. 7. The PGA champion fell down the leaderboard at 11 when he missed the green at the par-3 hole and failed to convert a two-footer for bogey.
The 2001 three-time winner clawed back with back-to-back birdies at Nos. 14 and 15, but a bogey on the 17th gave him his 68.
'I was very happy with the round,' said Toms. 'It was my first competitive round of the golf course and I felt like I played it pretty well.'
Duval struggled from the beginning with a bogey at the first. He double-bogeyed No. 5 after driving out of bounds, and Nos. 7 and 18 when he found water.
'I played poorly,' said Duval, who shed the title of 'best player to never win a major' at the British Open. 'I'm glad the day is over.'