Jones, looking for his first Champions Tour victory, made a 15-footer for birdie to get to 4-under 140 at TPC Treviso Bay.
I rolled that baby right in, and it felt great, to be honest with you, he said. It was a good way to end the day.
The 4-under total is the highest score to lead in Naples since the tournaments second year in 1989.
Loren Roberts, the 2006 winner, Don Pooley and James Mason are tied for second.
Pooley looked like he would end his day with the lead. But he three-putted for bogey on No. 17, and double-bogeyed No. 18 after hitting his third shot in the water on the par-5.
Im glad it wasnt the last day, he said. Im glad I have a day to redeem myself.
Jones never made it on the PGA Tour, but prepared for the Champions Tour by winning 19 times in three years on the Sunbelt Senior Tour, which has an age minimum that includes golfers younger than 50.
In 2008, Jones was medalist in the Champions Tours qualifying tournament, then had 10 top-10 finishes in 22 starts. He won the qualifier at last years ACE Group Classic, then tied for eighth.
I was fortunate to play on the Sunbelt Tour for three years and get a lot of winning experience, he said. A golf tournaments a golf tournament. Its just nicer out here.
Roberts birdied Nos. 11, 14 and 17 to get to 4 under, but three-putted No. 18. His 71 was the 11th consecutive sub-par round at the tournament.
Its the second day in a row I probably played better than I scored, Roberts said. I made two bogeys, both three-putts. Those leave a bad taste in your mouth when you three-putt No. 18 to finish.
Mason, 58, was in the first group of the day and had the lowest score, a 67.
Pooley, 57, nearly held onto the lead, despite missing seven of 18 greens during the second round. He hit 16 of 18 in a first-round 68. Pooley is seeking his first win on tour since 2003.
I really want to win, get back to Hualalai (site of the season-opener for tournament champions), one of my favorites he said. And I just to win again. Its been a while, and Im getting old. So I want to do it.
Vicente Fernandez, who was tied for the first-round lead, bogeyed four of his first five holes on the back nine, and shot a 76. He is tied for 15th at even par.
Jay Haas, who fell out of the lead on Friday after a two-stroke penalty, had a double-bogey and three bogeys in his first six holes. He shot a 76 and is tied for 22nd at 1 over.