Scott McCarron fired an 8-under 64 to move into a tie for fourth place. He is joined at 20-under-par 195 by Woody Austin (65) and Tim Herron, who carded a 5-under 66 on the TPC at The Canyons.
Flesch began on the back nine at the TPC at Summerlin, one of three courses used for the opening three rounds. He began slowly with four straight pars. He sank a birdie on the par-3 14th and followed with a birdie on the 16th to move to 19-under.
The lefthander then dropped a shot at the par-3 17th, but came back to birdie the very next hole. Flesch birdied No. 1 to make it two in a row and get him to minus-20.
Flesch then notched consecutive birdies from the third and closed out his scoring with a birdie on the sixth.
'I really played well today. I shot 6-under, but I putted horribly,' said Flesch. 'I have just been hitting it so well of the tee and have wedges and shorts clubs in. I ran in some long ones, but I missed a lot of putts today I think I really should have made.'
Verplank teed it up on the Southern Highlands Golf Club and got off to a quick start with a birdie at the first. However, he stumbled to a bogey on the very next hole.
'I was disappointed in that to say the least,' said Verplank of his bogey on the second, his only bogey of the tournament so far. 'I pulled it about three yards left of where I wanted it to go and it went into the bunker. I hit a nice bunker shot and a nice putt, but it didn't go in.'
The 39-year-old Verplank carded birdies on the fourth and ninth to head to the back nine at 19-under. He birdied the 10th to make it two straight.
He came back to birdie the par-5 13th. Verplank was able to join Flesch in first place as he birdied the 17th and 18th.
'Today was a little trickier. The wind was definitely blowing early in the round and out here at Southern Highlands,' said Verplank. 'I don't think everybody is quite as familiar with this golf course as they are with the TPC golf courses.'
Appleby, who also played the TPC at Summerlin, opened with an eagle on the third, then birdied the seventh and ninth. Around the turn, he birdied No. 10 through 13 to make it five straight birdies. He capped his round with a birdie at the 16th.
'The key is to hit the ball well, create opportunities and make some of those opportunities,' said Appleby. 'At this tournament, you have to make a lot of birdies and that means getting the ball near enough to the hole where those opportunities can come.'
Bill Glasson fired a 9-under 63 to move into a tie for seventh place. He is joined at 18-under-par 197 by Robert Allenby, Craig Barlow, Mark Brooks, Jerry Kelly and Tim Petrovic. Bob Burns and Charles Howell III are one stroke further back at minus-17.
The cut line fell at 9-under-par 206 with 80 players advancing to the final two rounds, which will be played on the TPC at Summerlin.