Boasting second and third placings in major championships this season, Green led going into the final round after an eight-under 62 on Saturday.
But the 56-year-old Tanigawa came from two shots back to win his third career PGA Tour Champions victory, closing with a six-under 64, leaving 53-year-old Green with his third runner-up finish this year.
Tanigawa birdied the par-5 15th and 17th holes to pull away and win at 17-under 193 while Green bogeyed the 17th en route to his 68.
The victory was Tanigawa's first since the 2019 Senior PGA Championship.
"Boy, a little lost for words," Tanigawa said. "It's been a long time since 2019 to be in this position. Time goes by and you wonder if you can win again. To be able to do it, just over the moon."
Green was philosophical about missing a breakthrough win.
"It's nice to be competing and contending to do what I want to do," Green said. "It's just a shame that things just at the end there didn't really fall my way.
"I thought they were going my way there a little bit through the middle of the round, and probably my start today didn't really help me very much."
Darren Clarke (65) and Jason Caron (67) tied for third at 14 under.
Cameron Percy (66) was next-best of the Australians, tied 10th at 10 under.
Steve Allan (70) was a shot further back and tied 16th with Greg Chalmers (67) while David Bransdon (67) tied for 20th at eight under and Rod Pampling (67) and Stuart Appleby tied for 28th at seven under.
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