Finau recovered from an early bogey to card a five-under-par 67 at Albany Golf Club in the Bahamas.
Rahm endured no such drama as he posted the best round of the tournament with a blemish-free nine-under 63.
Jon Rahm broke into tears when he beat Tiger Woods in the Ryder Cup, the most meaningful moment of his career. "Knowing how much Seve means to me, having the five-footer to beat Tiger Woods, earning the first full point for the Europeans when it was looking kind of dark, there was a lot going on in my mind".
If there was one person for whom this weekend wasn't special, it may have been Woods. Woods earned seven top ten finishes but most importantly, he got back in the winners' circle for the first time in five years. It was quite terrible. I played so solid tee to green, didn't make any mistakes.
The 29-year old Salt Lake City golfer said he had also benefitted from a small adjustment to his putter as he seeks to make amends after losing out in a play-off in last month's WGC - HSBC Champions.
Speaking at the Hero World Challenge in the Bahamas, Woods said his desire was as strong as ever but acknowledged that his middle-aged and much-operated-on body was not able to do all the things his younger self could.
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"I'm so blessed and so thankful to have the opportunity to have everything turn my way".
Woods said that while he doesn't have definitive plans for his schedule next year, he won't play in as many events as he did in 2018.
"That's just part of the injuries I've had and the aging process and trying to deal with that and compete".
Rose (65), needing to at least have a share in a three-way tie for second to regain his World No. 1 status, did get to second at 15-under and he had an eagle, too, to help him.
Britain's Justin Rose was in sight of the world number one spot after a 65 but Finau denied him with a birdie at the last for sole possession of second.
That looked likely to happen heading into the final hole, when Finau sunk a 10-foot birdie to take clear second and knock Rose into third place. Kodaira moves back into the top 50 in the world, though he already was eligible for the Masters from winning the RBC Heritage at Hilton Head on the PGA Tour.