Vijay Singh, who held the second-round lead, carded a 4-under 69. He stands alone in second place at 18-under-par 201. Retief Goosen posted the round of the day with a 9-under 64 to climb into third place at 15-under-par 204.
Appleby began the day one stroke behind Singh, but that changed quickly. Appleby birdied the first before Singh dropped a shot at the second on the Plantation Course at the Kapalua Resort. With the change in fortune, Appleby led by one shot.
He maintained that lead when he two-putted for birdie at the par-5 fifth. The Australian then ran home a 55-footer for birdie at the seventh to get to 16 under. Appleby capped a bogey-free front side with a birdie at the ninth.
Appleby moved to 18 under and three strokes clear of the field with a 10-foot birdie on the 13th. However, he stumbled to his lone bogey of the day at the very next hole after a poor chip shot.
The 32-year-old responded in fine fashion as he converted back-to-back birdies from the 15th to get to minus 19. Appleby maintained a two-stroke cushion over Singh as he made a short birdie putt at the last.
'Today was not too dissimilar to the other days,' said Appleby, who last season won the Las Vegas Invitational. 'The course was playing pretty much the same as previous rounds. I've played solid golf through basically all three days.'
Appleby knows the front nine Sunday will be important if he is going to win this event.
'I think you need to get under par comfortably. You don't need to slip through the turn even,' Appleby said. 'I think someone might need to get 3- or 4 under early. I won't be worried about that. I'll be plugging away and literally letting the score unfold. That's what I've been doing the last three days. To get off to a good start, three- or four-under is good.'
Singh, meanwhile, fought a balky putter most of the round. He three-putted for bogey at the second, but managed to erase that mistake with a birdie at the fifth. He matched Appleby's birdies on Nos. 7 and 9 to head to the back side at minus 16.
Around the turn, Singh again three-putted for bogey, this time at No. 11. He rallied down the stretch with consecutive birdies from the 15th. The Fijian got up-and-down for birdie at the last to cap his round.
'I think I made all of my putts on Friday,' Singh said. 'I played quite nicely today though. I made six birdies out there. I'm playing well and hitting the ball well right now. I just need that putter to get hot like it did yesterday.'
Goosen, playing with Tiger Woods, scorched the front nine. He ran off four straight birdies from the third to climb to 10-under. After a par at the seventh, he birdied three of his next four holes to continue his move.
The South African birdied two of his last three holes to close his 64, which matches Singh's second round 64 as the best rounds of the week.
'Overall, I was happy with the round,' said Goosen. 'Obviously, it wasn't blowing as strong as Friday, which made it a little bit easier off the tees as well as iron shots into the greens.'
Darren Clarke posted a 4-under 69, including an eagle on the 17th as he holed out from the fairway. He stands alone in fourth place at 14-under-par 205. Woods fired his best round of the event with an 8-under 65. He is one shot behind Clarke at minus 13.
Scott Hoch and Kirk Triplett share sixth place at 11-under-par 208. U.S. Open champion Jim Furyk is joined in eighth place by Davis Love III. That duo stands at 10-under-par 209.