The Victorian carded a final round of 67 to finish four shots behind the winner, Brooks Koepka, and just one shot out of second place.
A third round of 63 gave Leishman the opportunity to contend for the title and, although he was unable to match the brilliance of Koepka, it is yet another fine week on the PGA Tour for the 35-year-old.
The performance was made even more meritorious in that it comes off the back of a disappointing week at Royal Portrush last week where he missed the cut by six shots.
Leishman's outward nine of nine straight pars contrasted with a back nine featuring only one par but five birdies.
The result betters his best previous finish in 2019 in which he tied for 3rd at the Sony Open in Hawaii.
Leishman improves to 11th in the FedEx Cup standings, earns a cheque for US$602,000.
His PGA Tour career earnings climb to just under US$26.9 million.
Cameron Smith rebounded from what was a disappointing Saturday to be the next best of the Australians with a final round of 68 to tie for 12th place with Adam Scott and Jason Day sharing 40th place.
A third round of 73 on Saturday saw Smith slip from a share of 2nd place but it was another very good week for the Queenslander as he looks to secure his automatic place in the International Presidents Cup side.
For the winner, Koepka, he extends his lead at the top of the world ranking by winning his 7th career PGA Tour title and his 3rd of the season.
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