Nigeria were in control throughout the first hour, but missed chances and paid the price when Bongani Zungu headed a 71st-minute equaliser with South Africa's first shot on target. However they came back strongly in the second half, showing vast fighting spirit to score in the 63rd and 66th minute to take the lead for one final time and shut out Cameroon.
William Troost-Ekong scored a dramatic late victor to send Nigeria into the Africa Cup of Nations semi-final at the expense of South Africa.
The Super Eagles showed terrific determination to hit back from 2-1 down and beat favorites Cameroon, 3-2, in the round of 16. "South Africans are not naturally mobile", he added.
South Africa had to rely on being one of the best third-placed teams after losing 1-0 to Ivory Coast and Morocco in Group D, either side of beating Namibia by the same scoreline.
Boosted by the talismanic presence of Liverpool winger Sadio Mané, Senegal remain one of the favourites to win the Africa Cup of Nations, despite scraping through the quarter-finals with a 1-0 win over Uganda.
Nigeria went back to their old style of play by playing from the flanks as Ahmed Musa and Samuel Chukwueze gave the South Africans wing backs a run for their money. "I don't think he's (Rohr) fooling anybody", Baxter told reporters Tuesday. Honestly, it is something that interests me, but the team comes first in everything.
"If I don't win the golden boot but won the trophy I'd be very happy because we are here to do that", Ighalo said ahead of Wednesday's clash against South Africa.
Moses Simon started in the big win over defending champions Cameroon in the Round of 16 and posted a decent outing before he was replace by Villarreal youngster Chukwueze, who made a bigger impact in the half an hour he was on the pitch.
The game looked set for extra time before Williams flapped at a cross to leave Troost-Ekong with a simple finish.
"This is special now, you're getting to the sharp end of the stick and it's people that think like winners who will end up winning to tournament".