The American stunned Botha's home fans when he sent the South African crashing to the canvas with just 37 seconds of the bout remaining.
The 43-year-old warhorse was not able to get to his feet, leaving Grant to celebrate the 48th victory of his 52-fight professional career.
Botha, contesting his 58th fight had dominated much of the bout and had Grant in huge trouble in both the seventh and 11th rounds.
But he missed the chance to finish the American off, and he paid the price as Grant dug deep in the final three minutes and dropped Botha with a powerful right hand.
"I knew I had the strength to knock him out in the 12th round," said Grant, beaten by Tomasz Adamek on points in their WBO and IBF title fight in March.