The Australian, who birdied six successive holes to charge from six strokes back, three-putted the 18th on the Blue Monster, but he still took the $540,000 (pounds 338,000) winner's cheque after Ernie Els and Greg Kraft later fared even worse.
With Elkington in with an 8-under 64 for 275 - and having dented the trailer with a swift kick to repay the course for its final hole - Els and Kraft each came to the 18th, one of the toughest closing holes on the PGA Tour, needing a par to force a play-off.
Els played an 8-iron from 154 yards that swung into clumpy rough just short of the water. The South African then left his chip short. Kraft, seeking his first official PGA Tour victory, succumbed to the pressure. He caught his 5-iron so fat that it splashed into the water about 20 yards short of the green. A bogey for 71 left him second.