Schaper (64) beat American Ryan Gerard (66) in the playoff after both players finished the tournament at 22-under-par in windy conditions at the Heritage La Reserve Golf Links.
Schaper, 24, has now finished second-first-first in his last three tournaments on tour after winning the Alfred Dunhill Championship last week with an eagle on the first extra hole.
He tied for second at the Nedbank Golf Challenge at Sun City the weekend before that.
"That's just insane," Schaper said. "The last three weeks have been incredible.
"I believe in myself now. I'm trusting my game and the work that I am putting in. I have got such a great team behind me, so everything is pretty solid at the moment."