Masters winner Mike Weir is alone in second at even-par 72, while surprise British Open champion Ben Curtis is in third place at 1-over-par 73, followed by PGA Champion Shaun Micheel, who is last at 3-over-par 75.
This event is reserved for the four major winners in 2003 and is a 36-hole stroke-play event. For the first time since 1992, all four of these combatants are first-timers.
Furyk, who earned his major triumph at Olympia Fields in June, missed a chance for birdie at No. 1 but picked one up at the par-5 second hole with a routine two-putt. He then dropped a shot at the third when he missed a 15-footer for par, but the story for the next few holes was his putter.
Furyk, who finished 14th on tour in putting average, missed makeable chances for birdie at the fifth and seventh holes. He finished off his front nine with a four-footer for birdie to get to 1-under par.
The U.S. Open champion made it two in a row with a 16-footer at the 10th. That birdie gave him a one-shot lead over Weir, a lead that Furyk would not surrender on Friday.
Furyk made par at the par-3 11th but cashed in on a 12-foot birdie putt at No. 12 for his fourth three in a row. He had another makeable birdie try at the following hole but settled for a par, still holding his two-stroke advantage.
It took one hole for Furyk to return to his birdieing ways. He laid up short of the par-5 14th green, but knocked a wedge to five feet. Furyk rolled home the birdie try to get to 4-under par and take a three-shot lead over Weir.
Trouble loomed for Furyk at the par-4 15th as his drive landed in the right rough. He had an awkward stance in a bunker but skipped his second short of the green. Furyk chipped four feet past the hole and sank the par-saving putt, which allowed him to keep his three-shot lead when Weir missed a five-footer for birdie.
Furyk drove into the left rough at the reachable, par-5 18th, so he laid up short of the green. His third came up 25-feet short of the hole, but he drilled the birdie putt to pad his lead.
'I hit one or two bad putts,' admitted Furyk. 'I've been fooled on a few reads. I've been fooled on the speed of the greens. I hit them on line, not quite hard enough.'
Weir, who became the first Canadian major winner when he donned the green jacket at Augusta, was solid on Friday but only made one birdie, a six-footer at the par-3 seventh. He made two impressive par saves on the front nine, a 20-footer at the third and a difficult chip from over the green at No. 8.
At the par-3 17th, Weir missed the green short and right. He pitched to six feet but missed the par save to fall to even-par on the round, five behind Furyk.
'You need to get in the fairway out here for sure,' said Weir. 'There are tough conditions out here with mud on the ball and the wind.'
Curtis, who was the lowest-ranked player in the field when he hoisted the claret jug this summer, struggled early with some bogeys, but rebounded with an eight-foot birdie putt at No. 15.
He parred out to stay within six of the lead.
Micheel, whose 7-iron into the 72nd green at Oak Hill was the shot of the year, seemed to have trouble reading the greens Friday at Poipu Bay. He double-bogeyed the fourth when he left his first play from the bunker in the sand and things did not get better.
By the time Micheel missed a six-footer for par at the par-5 15th, he was 4 over on his round. He birdied the last thanks to a great 4-iron approach, but it will still be a tall hill to climb for the PGA Champion as he trails the U.S. Open winner by eight.