Candie Kung carded a 73 to finish alone in third place at 8-under-par 208. Annika Sorenstam, Mi Hyun Kim, Patricia Meunier-Lebouc and Becky Morgan were one shot further back at 7-under-par 209.
Saiki, a runner-up on four different occasions in her LPGA Tour career, has put together three solid rounds at Locust Hill Country Club as she tries again for a breakthrough victory.
The 38-year-old had a slow start to her round with 10 straight pars before her third shot to the par-5 11th landed behind the pin and almost spun back in for an eagle. Saiki tapped in for her first birdie of the day and played her approach to 7 feet for a birdie at the very next hole.
At the par-4 13th, Saiki flew her approach over the green, but knocked her third shot in the cup for her third consecutive birdie to move two clear of the field.
Jones, a two-time winner of this event, was putting on the pressure with three birdies over her first 10 holes and drained a long birdie putt at the 14th to move to 11 under. Jones then hit her tee shot to the fringe at the par-3 15th to join Saiki atop the leaderboard.
Saiki persisted, however, but appeared to be in trouble at the par-5 17th. She found a fairway bunker off the tee and left her second shot in the rough. Saiki buckled down and played a remarkable third that stopped within 5 feet of the cup.
She ran home the birdie try and parred the 18th to carry a slim lead into the final round.
'Actually, I wasn't aware until the 16th green,' said Saiki of Jones' run up the leaderboard. 'I felt very comfortable with the way my round was going and I really didn't look at the leaderboard a whole lot today. I felt that I was in very good position shooting what I was shooting.'
Jones, who had made a couple of long birdie putts to move into contention, also tallied a birdie at the 17th, but sent her second shot into a greenside bunker at the last en route to a bogey for a round of 67 and 12-under-par 204 total.
'I like to be one shot back,' said Jones. 'I can handle one shot ahead. I've been there enough times to go ahead and go home and not be as nervous about it or have anxiety about it or lose any sleep over it. I'm very pleased with my round today and looking forward to tomorrow.'
Sorenstam, who has never won this event, hit her approach to 3 feet for a birdie at the third and after a bogey at the ninth, the Swede dropped her second inside 5 feet for a birdie at the 10th.
She found trouble with another bogey at the 14th, but countered with a birdie at the 17th to finish six shots off the pace after a round of 71.
Defending champion Rachel Teske shot her third straight 70 to join Juli Inkster and Catriona Matthew at 6-under-par 210.