Paul Goydos also posted a 63 and that moved him into third place at minus-8. David McKenzie (68), Dean Wilson (67), Charley Hoffman (67), Bernhard Langer (65) and Frank Lickliter (66) share fourth at 7-under-par 133.
Points started on the back nine and quickly found trouble, finding the right rough off the tee at the 11th. From there, he blasted his second well over the green and under a tree.
He pitched it back onto a hill behind the green and left his next shot on the hill as well. Points finally got it up and down from there, but the double-bogey dropped him to minus-3.
Points found a greenside bunker with his approach on 12. After blasting out, he two-putted for bogey. He began to right the ship with a two-putt birdie on the par-5 14th of the Resort Course at LaCantera Golf Club.
'Well, it started out terrible, could not have started out any worse,' Points admitted. 'I just made a couple of loose swings and got a couple of bad breaks and I was struggling.'
The 29-year-old dropped a wedge within 6 feet on 16 and sank the birdie putt. At the 18th, his pitching-wedge approach shot came to rest 7 feet from the hole.
Points, a three-time winner on the Nationwide Tour, dropped that birdie effort in to get back to even-par for his round and minus-5 overall. He ran home a 25-footer for birdie on two, then sank a 12-foot birdie effort on four.
He came right back with a 6-foot birdie putt on five to get to 8 under. Points used a pitching-wedge for his second shot at eight and stuck it eight feet from the hole. He sank that birdie putt to finish at minus-9.
'I kind of got it together. I had a good drive on the par-5 (14th) and I kind of figured something out with my swing. It was nice to get back to even- par through nine holes so I didn't feel like I necessarily gave a ton back to the field,' said Points, who has needed just 51 putts through two rounds. 'Then I made the turn and started making some more putts.'
Axley was hot from the start. He knocked in a 9-foot birdie putt on the first, then ran in a 5-footer for birdie on four.
The 32-year-old caught fire on the seventh. Axley converted an 8-footer for birdie there, then a 5-footer for birdie at the next.
Axley hit wedge to 8 feet on nine, and sank that to make it three in a row. He pitched to 3 feet on the par-4 11th and made that putt for birdie. Axley joined Points in the lead when he two-putted for birdie from the fringe on 14. He parred the final four holes to remain tied for the lead.
'Today was a pretty stress-free day,' admitted Axley, a tour rookie. 'It seemed like all my birdie putts I did make were between 8 and 12 feet without much break.'