Slay edged past Kazakhstan's Gennadiy Laliyev on Friday morning and then beat former world championship bronze medallist Adem Bereket of Turkey 3-1 in the evening.
Slay caused a major upset on Thursday when he beat reigning Olympic champion Bouvaissa Saitiev of Russia in the elimination pool.
Saitiev is widely considered the best freestyle wrestler in the world but Slay said he kept his feet firmly on the ground after his win.
"I enjoyed the exuberance for a couple of hours and then I put it behind me," he said. "It was just a stepping stone."
Slay and Laliyev finished at 2-2 but the American was given the decision because of the Kazakh's greater passivity.
"It was a little nerve-wracking, but I knew that he had to come to me and that I was would get the decision if it went to passivities," the American said.
The religious Slay, 25, said his progress owed a lot to his faith. "God deserves all the glory," he said.
Slay is bidding to become the first American gold medallist in the welterweight division since Kenny Monday in 1988 and will meet Alexander Leipold in the final after the German scored a bruising and controversial 3-1 win over Moon Eui Jae of South Korea.
"If I keep wrestling the way I'm wrestling -- to my potential -- I'll win tomorrow night," Slay said. "I know I can beat these guys. I wouldn't have come to the Olympic Games if I didn't think I could win."
Wrestling
