Gumberg carded a bogey-free four-under-par 68 in his final round to finish on 12 under for the tournament, level with South African Williams (69), who was on 14 under-par before a double-bogey on the par three 17th forced a playoff.
Both players parred the first extra hole before Gumberg, ranked 669 in the world, sunk a birdie on the second to take the title, his first on the DP World Tour. It will earn him an exemption on the tour for this season and the next.
"I knew today was going to be tough with the rain and tried to go one shot at a time. It was a solid round of golf and I'm just so thankful to be standing here," an emotional Gumberg said.
"It means everything, I never got this far in my dreams, so I am lost for words. It was what we practise for, all the long hours, it makes it worthwhile."
Frenchman David Ravetto (70) finished third on 10 under-par.
Overnight leaders Daniel Brown from England and Scotsman Connor Syme carded disappointing 75s in their final round to finish in a group of six players tied for fourth.
