The pair is knotted at 8-under-par 208 and is one ahead of John Kimbell, who posted a 1-under 71 in round three. Justin Bolli carded a 5-under 67 on Saturday and is alone in fourth at minus-7.
Wind was the story on Saturday at Kinderlou Forest Golf Club. Only 13 players managed to break par in round three and the player whose under-par score mattered the most was Jones'.
It did not look like Jones was headed to a share of the 54-hole lead as he tallied back-to-back bogeys at three and four. He rebounded with a birdie at the sixth, but then went on a par run that kept him near the top of the leaderboard.
Jones' big move came at the par-5 11th. He hit an 8-iron from 195 yards out to 30 feet and rolled in the eagle putt to reach 7 under par for the championship.
He birdied the 14th to get to minus-8 and parred out for his share of the lead.
'I rolled it pretty good today,' said Jones. 'My speed is getting better and if that keeps happening I should be good. I haven't played well this year so it's nice to be in contention. This year has been a struggle but one win could turn that all around.'
Dickinson, who tallied only one bogey through the first two rounds, birdied the second, then double-bogeyed three and bogeyed four. He closed his front nine with birdies at seven and nine, but was up and down on the second nine.
He bogeyed the 10th, but came back with a birdie at No. 11. Dickinson dropped another shot at 13, but quickly reclaimed the lead with a birdie at the par-5 14th.
Dickinson lost sole possession of the lead with a bogey at the par-3 15th.
'It was brutal today,' acknowledge Dickinson. 'I was all over the place. I'm actually glad I shot one-over and in the position that I am. My mind got a little out of sorts there on the back nine. I just tried my hardest to stay focused and stay in the present.
'It was really windy and the course was really fast. On top of that the course is so long. Man, it was a long day. I'm just glad I got out of there without hurting myself.'
Aaron Watkins fired a 6-under 66 and is tied for fifth place with Aron Price (71), Chez Reavie (71) and former PGA TOUR player Carlos Franco (72). The group finished at five-under-par 211.
John Huston, a seven-time winner on the PGA TOUR, struggled to a 1-over 73 on Saturday and is knotted in ninth place with Scott Gutschewski (68), Tom Byrum (69), Jeff Klauk (68), Hunter Haas (69) and Steve Allan (70). They completed three rounds at minus-4.