'I'm hitting the ball a little better so I'm giving myself a lot of chances, so I think that's the main thing,' said Wilson, who is currently 150th on the PGA Tour money list. 'I haven't been doing that all year.'
Purdy, who matched the course record with a 61 on Thursday, managed a 1-under 69 in the second round to come in at 10-under-par 130. J.J. Henry, David Peoples, John Senden and Ryan Palmer share third place at 9-under-par 131.
Wilson was three shots back to start the day at LaCantera and hit a wedge to 15 feet for a birdie at the par-5 first. Wilson then parred his next five holes before his second shot to the par-4 seventh stopped within 4 feet of the hole for a birdie.
The 34-year-old picked up steam on the inward half with back-to-back birdies starting at the par-4 11th. At the par-5 14th, Wilson reached the green in two and calmly took two putts for another birdie.
'That back side might be a little more scorable there just because you have a par-5 that's reachable,' said Wilson.
Wilson found trouble on the green at the very next hole and three-putted the par-4 15th for his only bogey of the day.
He recovered at the 18th and knocked his approach inside 2 feet for a kick-in birdie to complete his round.
'So far this year I haven't played so well and dug myself a pretty good hole the last couple of months, so I need to start playing better,' said Wilson. 'That's the main goal. I'm going to be out playing every event until I make my money.'
Purdy was on fire in the opening round, but the 31-year-old got off to a shaky start on Friday with three birdies and three bogeys over his first nine holes.
Purdy made a move to catch Wilson with a birdie at the par-4 11th and another birdie at the par-5 14th lifted him to 11 under. He struggled coming in, however, with a bogey at the par-3 17th to finish one shot off the pace.
'It was a complete reversal from yesterday,' said Purdy. 'Today I had a lot of adversity and yesterday I had none.'
Henry, who tied for second at this event in 2001, collected four birdies and a bogey for a round of 67.
'I enjoy coming here,' said Henry. 'I live about four and a half hours from here. I always enjoy coming.'
Aaron Barber and Scott Simpson tied for seventh place at 8-under-par 132. Jerry Kelly, Justin Leonard, Duffy Waldorf and Patrick Sheehan followed at 7-under-par 133.
Defending champion Tommy Armour III finished eight shots off the lead in a group at 3-under-par 137.
The 36-hole cut fell at 2-under-par 138 with 79 players qualifying for the weekend. Among those who failed to make the grade were former major champions Rich Beem and Jose Maria Olazabal.