Willett closed with a flawless four-under-par 68, which included birdies at holes two, nine, 16 and 18 and no bogeys.
An outward nine of 40 in his second round, when problems with his back required on-course treatment from the Tour physiotherapist, effectively put paid to his attempt to win the title in Sun City for a second successive year.
But weekend rounds of 70 68, tacked on to an opening pair of 67 75, earned a top-5 finish for the Yorkshireman who finished second to world No 3 Rory McIlroy in the 2015 Race to Dubai standings.
His fellow Sheffielder Matt Fitzpatrick birdied holes one and two on the final day - the latter for the third time in four rounds - and looked to be set for yet another top-10 finish.
But he collected three bogeys in his closing six holes, as well as a birdie at the 14th, to sign for a level-par 72.
His 286 aggregate (69 77 68 72) left him in a tie for 16th.
Leishman (68 68 66 67) finished 19 under par for the week and six shots clear of second-placed Henrik Stenson, of Sweden to claim his first European Tour title and complete an Australian double following compatriot Nathan Holman's win in the Australian PGA Championship earlier in the day.
England's Chris Wood was a distant third on nine under with defending champion Willett, Victor Dubuisson, Robert Streb and Branden Grace joint fourth on eight under.
Leishman began the day with a one-shot lead and found himself three ahead when he birdied the seventh and playing partner Stenson bogeyed the same hole after failing to get up and down from a greenside bunker.
World No 7 Stenson bounced back with a birdie from 15 feet on the eighth and both players two-putted the par-5 ninth for birdie to give Leishman, who lost a play-off for the Open at St Andrews in July, a two-shot lead heading into the back nine.
Leishman and Stenson also two-putted the par-5 10th for birdie before Leishman extended his lead thanks to a superb approach to the 13th, which span back to within inches of the hole.
Stenson saved par from over the green to keep his hopes of a second title alive, but the 2008 champion could not repeat the feat after a wayward drive on the 15th, where another birdie from Leishman took the 32-year-old five clear.
Leishman, who defeated world No 1 Jordan Spieth in the singles in the Presidents Cup in October, moved further ahead with a birdie on the 16th and although Stenson chipped in on the next, the result - and destination of the first prize of £825,000 - was never in doubt.