Axley, who has never won on the PGA TOUR, is in the top-10 heading into the final round for just the second time in his career.
After three rounds of the Chrysler Classic of Tucson earlier this year, Axley was in ninth, but slid into a share of 24th after an even-par 72 in the final round. That tie for 24th stands as his best career finish to date.
'I did play in the final group,' said Axley of his win last year on the Nationwide Tour. 'The week I won, I was in the next to last group and we played 36 on Sunday so it was no re-pairing, but the Tour Championship I did play in the final group and played well.
'You know, drawing back from the Nationwide Tour, definitely it's a very competitive tour and it helps, you know to play in the final group in twosomes and feel the nerves and being the last group out there so, yeah, it definitely helps to have been in that position before.'
Ted Purdy and Chris Riley each posted rounds of 6-under 64 to move into a share of second place at minus-12. They were joined there by Frank Lickliter, who closed with four birdies in the last four holes.
Dean Wilson, who collected his first tour win earlier this year at The International, is alone in fifth place at 11-under-par 199 after a Saturday 66.
Justin Rose, who shared the first-round lead, carded a 5-under 65 in round three and was joined in sixth place at minus-10 by Charley Hoffman (67).
Axley, a tour rookie, got off to a quick start with birdies on the first and third on the Resort Course at LaCantera Golf Club. A birdie on the par-4 eighth gave Axley a two-shot lead at minus-12.
The 32-year-old parred five straight holes from the ninth. With Purdy and Riley within one shot of his lead, Axley birdied the par-5 14th to move two clear.
Axley drove the par-4 16th and two-putted for birdie from over 50 feet out. He then dropped his tee ball within 3 feet at the par-3 17th. Axley kicked that in for birdie then left himself five feet for birdie at the last. He sank that putt for his third straight birdie and a four-stroke lead after 54 holes.
'I've been playing well for the last few weeks and it seems like my ball has ended up on the right side of the hole this week and I'm making a few putts,' Axley admitted. 'The only stressful thing about today is that I did not make many 10 to 12 footers.'
Purdy, whose lone win came at the 2005 Byron Nelson Championship, opened with a birdie on one. He notched back-to-back birdies from the fifth. Three more birdies on the back nine got Purdy to minus-12. He closed with two pars in a row to cap a bogey-free round.
Riley collected four birdies over the first seven holes to get to 10 under. After a bogey on 10, Riley notched consecutive birdies from the 13th and another birdie on 17 gave him a share of second.
Lickliter was 10-under after draining the third birdie of his round at the 11th. However, he double-bogeyed No. 12 to slide down the leaderboard. Lickliter flew back up the leaderboard with three straight birdies from the 14th. He also birdied the last to join Purdy and Riley at 12 under.
Brandt Jobe fired a 5-under 65 to move to 9-under-par 201. He was joined in eighth place by Paul Goydos (69) and David McKenzie (68). Danny Ellis and Bernhard Langer share 11th place at minus-8.
D.A. Points, who shared the lead entering round three with Axley, stumbled to a 2-over 72. That dropped him into a tie for 13th with J.P. Hayes and Anthony Kim.