Jones, who finished second at this event in 1993 and again last year, had five birdies and no bogeys to move to 11-under 202.
'I think it's my time here but I won't say it,' she said. 'I have a good feel for this course. I'm driving it straight and keeping it out of the rough.'
Jones began her flawless round one shot off the lead. On the par-3 2nd, she landed her tee shot two feet from the hole for a birdie two.
She sank an 18-footer on the par-4 8th and followed with three more birdies on the back nine to finish with a three-shot lead heading into the final round.
On the 14th, a hole she double-bogeyed in the second round, Jones used a 9-wood to land just short of the rough behind the pin. She two-putted for par.
'The par on 14 felt as good as the birdie on 13,' she said. 'Par is good on that hole.'
The 42-year-old is one round away from her second win this year and 12th overall.
'You know, probably what most likely I'll do is set a goal for myself to try to achieve and not try to protect any lead out there. I think that usually works pretty good when I'm in the lead or trying to maintain something,' she said.
Scranton, who shot a record-setting opening round of 64, managed a 70 Saturday to move to 8-under 205 and stand alone in second place. She birdied the 18th to finish one shot ahead of a group of players at 7-under that includes Betsy King, who won here in 1990 and 1991, and 1997 champion Michele Redman.
'I made some good saves when Rosie looked like she could have pulled away,' said Scranton. 'I had a great sand save on 14 and then had a really tough chip on 16 with my feet in the bunker and the ball right in front of a dandelion. That was a really good shot.'
Karen Stupples, who shared the lead with Scranton at 7-under heading into today's round, shot a 73 to finish six shots off the lead at 5-under 208.
Defending champion Annika Sorenstam is nine shots off the lead after a round of 70.
Full-field scores from the Sybase Big Apple Classic