Appleby stands at 28-under-par 259, which sets a new 72-hole record by two strokes. Scott McCarron owned the previous 72-hole mark of 261, which he set in 2001.
Steve Flesch, who shared the overnight lead, stands alone in second place at 27-under-par 260, followed by McCarron at 25-under-par 262. Robert Allenby is alone in fourth place at 24-under-par 263.
Appleby, who began the day one stroke behind the leaders, birdied the first but stumbled to a bogey at the next. The Australian recovered with back-to-back birdies from the third to climb to minus-24.
He came back with a birdie on the par-4 sixth and capped his opening nine at the TPC at Summerlin with a birdie at the par-5 ninth that gave him the lead.
Around the turn, Appleby birdied the 11th to move two strokes ahead of Flesch. Appleby came right back with a birdie at the next to extend his lead to three strokes.
The three-time winner on the PGA Tour followed with another birdie on No. 13 to remain three strokes ahead of the field. However, he stumbled to a three-putt bogey on the 14th and his lead dropped to two strokes.
Appleby moved back to 29 under with a birdie on the par-5 16th. Flesch, who had run off 10 straight pars, began to pressure Appleby. Flesch birdied the 15th and 16th to get to 27 under, but he could only manage pars on the final two holes.
Appleby meanwhile tripped home. He bogeyed the last to drop his lead to one stroke heading for the final round.
'I like the way I'm playing and I'd like to get it 6 or 8 under tomorrow, said Appleby. 'I'm pleased to be in this position. I like the way I'm playing.'
Flesch opened with birdies at the second and the fourth, but then parred 10 consecutive holes. His two late birdies helped him to a round of 4-under 68.
'A four-birdie, no-bogey round is pretty mundane on this course,' said Flesch. 'Tomorrow I want to convert the opportunities I had today. I know I haven't played my best golf yet. I know I have it in me to run the table again.'
Steve Lowery fired a 7-under 65 to move into fifth place at 23-under-par 264. Verplank, who had moved to within two strokes of the lead on the back nine, is one stroke behind Lowery at minus-22. Paul Goydos, Woody Austin, Charles Howell III, Mark Brooks and Tim Petrovic share seventh place at 20-under-par 267.