Ramsay shot a 7-under 65 to move past overnight leader Pablo Martin of Spain (73), Sunshine Tour Order of Merit winner Anders Hansen of Denmark (69) – who finished a stroke back in third – and finally Kapur (67).
Ramsay had a putt for the championship on the last at the Pearl Valley Golf Estates but it went fractionally left, forcing he and Kapur to go back up the par-5 18th for the playoff.
Kapur had to lay up in the playoff with his fourth shot – a chip from the fringe – landing within two feet. Ramsay reached the green in two and his 15-foot eagle putt came up just short, enabling him to tap in and raise his arms in triumph.
“I had no thought of laying up, because I was so sure of myself over the shot,” Ramsay said.
Ramsay clinched his playoff spot at the 17th, sending his approach over the water on to the green and sinking a 15-foot putt.
“I hit an 8-iron in, and I couldn’t believe it cleared the water,” he said. “My heart was in my mouth.”
Martin, who won last week’s Alfred Dunhill Championship, bogeyed the third and never recovered, managing only one birdie. A bogey at the 17th saw him finish joint sixth with Darren Fichardt of South Africa (66).