Atwal has not won anywhere since his maiden US PGA Tour win in 2010 and his best finish this year is a share of 19th place at the St. Jude Classic in June, but the 39-year-old was sublime en route to a seven-under-par 63 on the Seaside Course.
It moved Atwal, who has made just 11 cuts in 25 starts this year, to a 10-under-par total 130, one shot clear of host and 2012 US Ryder Cup captain Love (66) and veteran Furyk (65) at nine under.
US PGA Tour rookie and overnight co-leader Bud Cauley was two shots off the pace after following up his opening-round 62 with an even-par 70, in a share of fourth place with Americans David Toms (67) and Australian Gavin Coles (65) at eight-under.
American Michael Thompson (68) was in a group of six players tied for seventh place, three shots behind Atwal.
At 175th on the tour money list, Atwal will need a high finish either this week or next in the season's final tournament to return in 2013.
He was in a similar situation late in 2010 before he won his maiden title and earned exempt status until the end of 2012.
"I'm in a desperate situation," Atwal said. "I got no choice other than to either win or finish in the top two. I think my caddie figured that out so I just got to grind it out.
"I felt really calm out there, and the putter is starting to work. That was the missing link in the last few tournaments that I played."
Love III is full of confidence on the greens at his home course with a new belly putter, giving him a great chance to win his 21st US PGA title. His last victory came in 2008.
"I'm hitting the ball real well," Love III said. "I wouldn't say I've gotten everything out of the way. But it's my home course and I kind of know my way around it, so hopefully I can keep it going."
Furyk, who has suffered heartbreak defeats in the US Open, WGC Bridgestone and Ryder Cup this year, put himself in good position for the title. His 65 was bogey-free and featured four birdies in a six-hole stretch on the back nine.
Fijian former world number one Vijay Singh and Australian Jason Day are among a large group four shots off the pace.