The American made six birdies in a bogey-free 66 to move to 105th in the updated Race to Dubai Rankings in partnership with Rolex, with the top 116 projected to earn their playing rights.
Hanna had been four over for his first ten holes on Thursday, with five bogeys, but responded with four birdies before a closing bogey left him one over for his round.
A 67 on Friday and 69 on Saturday had him seven under and Sunday’s flawless card saw him to 13 under and safe for next season.
“It’s been a long year,” he said. “Been waiting for a round like today and it’s special to have it when it meant as much as it did today.
“I was very frustrated (on Thursday) because if you were going to design a course for me, this is it – wide, Bermuda grass - and I just got off to a terrible start.
“I switched putters coming into the week and somehow got it turned around. That last eight holes on Thursday is the reason I’m here right now.
“I took advantage of a perfect course for me. Every week we play tons of rough and driving is certainly not my strong suit, but I was able to get a lot of wedges which definitely is my strong suit and took advantage of it."
A tie for fourth, three shots behind champion Adrian Meronk, was Hanna's first top-ten finish since December's Investec South African Open Championship, where he finished in a share of fifth place.
“The results might not show it but I’m certainly a better player than I was last year, I’m always right around the cut line… just was waiting for a round like today where everything kind of went my way.
“I’m just fortunate to be standing here – if you’d told me this on Thursday through ten holes, I’d have been shocked.”