The Australian sits in sole second at 10 under midway through the tournament at the Newport Country Club, where Fujita (66) is attempting to earn his first victory on American soil.
Senior PGA champion Richard Bland fired a 64 to move into third place at eight under, tied with Steve Stricker (66).
Stephen Ames (68) is fifth at seven under. Two-time US Open champion Retief Goosen had his second straight 67 and is among three players at six under.
Frank Bensel, who made back-to-back holes-in-one on Nos.4 and 5 in the morning, finished with a 74 that left him at 9 over and missed the cut by seven.
An 18-time winner in Japan, Fujita had never shot in the 60s in four previous PGA Tour Champion Tour starts, never finished in the top 120 of a PGA Tour event or in the top 30 of a major. But he's played a nearly flawless 36 holes on the 7,024-yard, par-70 A.W. Tillinghast course.
"I was lucky yesterday, and I didn't expect to play this well," said the 55-year-old Fujita, who birdied three of his first five holes on Friday.
"I didn't expect that at all. I surprised myself a little bit. But it's only day two, and I want to continue to play consistent and not get too high or low and see where it takes me."
Fujita was the only player to reach 12 under during the round, making a birdie on No.2, his 11th hole. But he made a four on the par-3 fourth - his only bogey of the first two rounds - and then parred his way in.
Green made the turn from No.18 to No.1 with three straight birdies. He parred his last seven holes.
Stricker shot 66 for the second day in a row - his fourth consecutive nine at 33. But the 2019 US Senior Open champion said it was like playing a different course than in the afternoon, when the wind often does a 180-degree switch.
"We came out with soft conditions yesterday. Well, today we came out with completely the opposite wind to what we've seen the course in," he said.
"I haven't seen this course in this wind before. … It was a challenge. There are some holes that played a little bit easier, but some of the holes that played easy yesterday were difficult today."
Cameron Percy is at five under after posting a brilliant five-under 65 on Friday.
The Australian marked seven birdies and back-to-back bogeys on 17 and 18 to be tied ninth.
Defending champion Bernhard Langer, the 66-year-old who tore an Achilles tendon earlier this year, shot 72 and made the cut on the number.
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