Produced an incredible last-day charge and then won a play-off to lift the Visa Argentina Open in March and with it book a ticket to The 152nd Open.
Andersen, ranked 271st in the world at the time, looked out of the running when he set off in the final round six off the pace and played his opening six holes in two-over-par to lose further ground.
But the 25-year-old then birdied eight of the next nine and finished with another for an inward 29 and a 63, the low round of the day by three.
Norway’s Kris Ventura then joined him on 17-under-par and was on the par-5 18th green in two, but three-putted.
Both then birdied the first extra hole, but when Andersen produced another at the next it was all over.
The event was part of the Korn Ferry Tour for the first time and it was the former Arizona State University student’s first victory on the circuit.
“Winning is just so hard in golf,” he said.
Last October he led the Korn Ferry Tour Championship after an opening 64, but slipping to joint 10th meant he missed out on a PGA Tour card by four strokes.
“I’ve barely experienced links golf, so we’re going to have to gear up and get ready for that.”