Mark Pfeil had the low round of the day with a 64 to move into a share of third place. Pfeil was joined by Doug Tewell and Bruce Fleisher at 9-under- par 135.
Dougherty jumped out of the gate Saturday with two birdies over the first four holes at Egypt Valley Golf Club. He then added a birdie at the par-4 ninth to go out at 9-under par.
The 55-year-old, who is seeking his first victory on the Champions Tour since 2001, kept things going on the back side with a birdie at the par-4 11th and another birdie at the par-5 13th.
Dougherty faltered with a bogey at the par-4 14th but managed to recover down the stretch. He left his 7-iron 42 feet from the cup at the par-3 16th but drained the putt for a birdie. At the very next hole, Dougherty sank a 50-foot putt for his seventh birdie of the day.
'Two of the longest putts I've made in my life at 16 and 17,' said Dougherty. 'I tried to lag the one at 16 and then the one at 17 was pure luck. Overall, I didn't think I putted that well today.'
Dougherty had some kind words for Green, who he will join in the final threesome on Sunday.
'Hubert Green is a story all unto himself,' said Dougherty. 'He's a courageous man. I don't know if I could be doing what he's doing. We're all like a big family out here.'
Green, who was recently diagnosed with throat cancer, continued his solid play that saw him open with a 66 on Friday. He collected three birdies over his first nine holes to keep pace with Dougherty and hit a 5-iron to 25 feet for a birdie at the par-3 12th to move to 10-under.
He birdied the 14th but found trouble with a bogey at the very next hole. Green managed to counter with a tap-in birdie at the par-5 17th to remain well within reach of the lead.
'I'll play one shot at a time tomorrow,' said Green. 'I'll look at the leaderboard and see where I am quite a bit. If you don't look at the board, you don't want to win.'
Mike McCullough fired a 7-under 65 to finish at 8-under-par 136 along with David Eger, Eamonn Darcy, Tom Wargo and first-round leader Morris Hatalsky.
D.A. Weibring and Dave Stockton were one shot further back at 7-under-par 137.
Gil Morgan, Bruce Lietzke and Mike Smith finished tied for 13th at 6-under- par 138.
Defending champion Jay Sigel struggled on Saturday with a round of 76. He finished in a tie for 59th at 2-over-par 146.