U.S. Open champion Geoff Ogilvy is alone in second at minus-4. Tiger Woods, the British Open and PGA Championship winner, struggled to a 2-under-par 70, while 2003 Masters winner Mike Weir is in fourth at minus-1 at Poipu Bay Golf Course.
Furyk, who won by eight here in 2003, rolled in a 10-footer for birdie to get his round going. At the par-5 sixth, he two-putted for birdie to get to minus-2.
The world's No. 2 player two-putted for birdie from the fringe on the 13th. Furyk grabbed the lead with a 10-foot birdie putt on the 17th. He pitched to 9 feet at the last and sank that putt for a closing birdie.
'Obviously I'm happy with where I stand after the first round,' stated Furyk. 'I did a good job of getting the ball in the hole and scoring. I kept the ball in the fairway most of the day. I was putting from long distance for a lot of the day, but my putting was very good today.'
Ogilvy, the only one of the four making his first appearance here, grabbed the early lead with a solid front nine. He sank 6-foot birdie putts on the second and fifth. Ogilvy came back with a 15-foot birdie putt at six to move atop the leaderboard at minus-3.
The Australian two-putted for birdie at 13, but trouble loomed. Ogilvy's tee shot went well long of the par-3 17th.
Ogilvy left his chip shot short in the rough He nearly holed his third, but needed to sink a 4-footer for bogey that dropped him to minus-3. He two-putted for birdie from 40 feet at the last to end one behind Furyk.
'I played quite well. I didn't hit too many bad shots, just one bad shot on 17, the tee shot,' admitted Ogilvy. 'Apart from that, I was pretty happy with it.'
Woods, who is coming off second-place finishes in China and Japan, was up and down all day. He opened with back-to-back birdies from the first, but tripped to a bogey at the fourth after knocking his second over the green.
The 30-year-old kicked in a short birdie putt on six and made it two straight as he poured in a 20-footer for birdie on seven. Woods found a fairway bunker of the tee at eight and that led to his second bogey.
Woods dipped to minus-1 with a bogey on the short par-4 13th after his tee shot found the water right of the green. He closed with a two-putt birdie at the last to end at minus-2.
'Nos. 1 and 18 were solid. The other 16 holes were just not very good,' said Woods, who has carded 11 straight sub-par rounds at Poipu Bay. 'I struggled today. It was frustrating. Somehow I was able to shoot 2 under. I don't know how I did that. I'm only three back, so hopefully (Wednesday) will be a little better day.'
Weir knocked his second shot within inches at the first and kicked that in for birdie. He came back with 3-foot birdie putt on six.
The Canadian faltered to a double-bogey at the eighth. He hit his second shot over the green and had to take a penalty drop before chipping on and two-putting for double-bogey from 13 feet. Weir got one stroke back with a two-putt birdie on 13.
'I didn't strike the ball as solidly as I've been doing the last little bit, so that was a little bit disappointing,' Weir said. 'I didn't get the ball in the fairway...Outside of that, I hung in there pretty good and hope to have a good one tomorrow.'