Rose, the first-round leader, carded a three-under 68, while Wilson posted a five-under 66. They completed 36 holes at 11-under-par 131 and lead by two strokes.
Webb Simpson, who currently leads the race for the FedExCup, matched Rose's 68 and is alone in third at minus-nine. John Senden is one stroke further back at eight-under-par 134 after shooting 66 on Friday.
This is the third of four events in the PGA Tour playoffs and only the top 30 players on the points list will tee it up at East Lake next week for the Tour Championship.
Rose is projected to jump to No. 4 in the race, while Senden would jump to 24th. If things hold as is, former PGA Champion Y.E. Yang (No. 28) and Kyle Stanley (No. 30) would fall out of the top 30 and miss the Tour Championship.
Wilson, who lives nearby and plays out of Cog Hill, and Rose were the only two players that led during the second round. Rose had five pars and a birdie, on No. 3, in the first six holes. He was two clear of Wilson at that point.
Wilson, who was four groups ahead of Rose, tripped to a bogey on the first, but recovered that stroke with a birdie on the fifth.
After Wilson birdied eight and nine, he rolled in a four-footer for birdie on No. 10 to grab the lead from Rose, who stumbled to a bogey on the seventh.
Rose came right back with an eight-footer for birdie on the eighth to join Wilson at minus-nine. Wilson made his fourth consecutive birdie as he sank a 15-foot birdie effort on the par-five 11th.
At the par-five ninth, Rose responded with a short birdie try that again gave him a piece of the lead at 10-under as Wilson parred three straight from the 12th.
"This was an amazing up and down, one of the best of my life," Wilson said in an interview with the Golf Channel of his par on No. 14. "I was trying to fly it about 15 feet on the green and just try to make a 20-footer. It looked like it landed on the fringe and I left myself a little four-footer."
There was a two-stroke swing when Wilson rolled in a 24-footer for birdie on the 15th to get to 11-under. Just after that, Rose stumbled to a bogey on the 13th to slide to minus-nine.
Wilson had a stellar par-save at the last to cap a run of three straight pars to finish at minus-11.
"It was half-buried and I almost hit it too good," Wilson told the Golf Channel about his bunker shot on No. 18. "I expected it to come out a little lower and catch the slope a little better, but I hit that just perfect. I had an awkward putt that was a triple-breaker."
Rose fought back with a 32-foot eagle putt on the par-five 15th. He took the lead by himself with a 15-foot birdie effort on the 16th. After a par at 17, Rose missed the fairway on No. 18 and that led to a closing bogey, which dropped him into a share of the lead with Wilson.
"You never quite know what to expect after playing so well in the first round," admitted Rose, who shot 63 in round one. "A couple spells in my round it went a little bit flat, but I managed to create some momentum, get a couple birdies around the turn and then had a pretty good finish with eagle at 15 and birdie at 16. So I'm happy with the day."
Robert Allenby (67) and Bill Haas (66) share fifth place at six-under-par 136. Matt Kuchar (65), Geoff Ogilvy (68), David Toms (66), Brandt Snedeker (66) and Keegan Bradley (66) are one shot back at minus-five.
NOTES: With just a 70-player field this week, there is no cut...Rose has won one of the previous eight times he had a piece of the 36-hole lead and that win came last year at Aronimink in the AT&T National...Wilson owns a piece of the 36-hole lead for the fourth time on the PGA Tour and he is 1-2 in the first three...Defending champion Dustin Johnson managed a one-over 72, but is tied for 64th at plus-six...Among those on the outside of the top 30 at this point are reigning FedExCup champion Jim Furyk along with former major champs Zach Johnson, Yang and Lucas Glover...Steve Stricker, who is the only player to have competed in every round of the PGA Tour Playoffs for the FedExCup, withdrew after the second round.