They beat the hosts, Russia, with 2-0 in a thrilling quarterfinal encounter.
The South Africans will now face Belarus for a place in the final and in the other semi-final Turkmenistan play Finland on Friday.
The South Africans was put under pressure by Russia in the first half but Amajita turned on the heat in the second half scoring two quick goals.
It was the Russians who started the game with purpose and almost scored an early goal in the first minute.
The South African goalkeeper Dumisani Msibi, who was Man of the Match came off his line to avert danger.
Winger Yevgeny Markov was dangerous on the left wing and his cross in the 7th minute was well saved by Msibi as the hosts continued to threaten.
Siyanda Ngubo and Pule Maraisane was brought on after half time to add to the attack.
The move paid off when Maraisane received a pass from Ngubo before scoring South Africa's first goal in the 50th minute. Just five minutes later, Siphelele Luthuli made it 2-0.
It could have been 3-0 seconds later but Ngubo's well-taken shot went wide as Amajita upped the tempo.