However, Paul Treu's side had the final say, just as they did at the same stage of the competition in Dubai a week ago and ensured a repeat final against New Zealand.
Kabamba Floors immediately had the crowd on its feet when Schalk van der Merwe ripped the ball from Charles Amesbury and set the blond flanker on an 80-metre run.
England struck back on the five-minute mark as they stretched the Boks from side to side until Michael Hills trotted in untouched to level the scores.
Golling kicked a vital conversion from the sideline to put his side ahead by two, a lead they kept into the half-time break.
The second half turned out to be a massively tense affair, with both sides taking way too much contact and tempers rising at stages, prompting referee James Jones to talk to both captains to calm their players.
The Boks broke the deadlock as they stretched England to all sides, and finally found a gap where try-scoring machine Phillip Burger sped in for what turned out to be the winning try.
There was further tension when Dusty Noble pushed Amesbury outside the field of play and was yellow carded for his efforts.
Down to six men, Kabamba Floors won a vital penalty at the ruck shortly afterwards to ensure the Boks could simply put it out for the victory.
In the other semi-final, New Zealand stunned World Champions Fiji to pull away to a 29-0 lead before Fiji scored two consolation tries to lose 29-12 in their play-off match.
England earlier swept into the semi-finals with a comprehensive 24-0 quarter-final victory over Samoa at Outeniqua Park.
The win was clinical in its execution, but put England on a collision course with the tournament's form side South Africa, who beat them at the same stage in Dubai last week and were just as impressive in sweeping aside day one's giant killers Tunisia 38-0 in their quarter-final.
Hard-running Michael Hills opened the scoring for England in the third minute as he pumped his way through the Samoan defence for a powerful try and James Haskell extended the advantage by cutting his way through the defence on a switch to take England into the break 14-0 up.
Haskell added a second after the break before Dominic Shabbo finished off the rout with a late try to put Mike Friday's side through to the semis.
South Africa's victory was just as creditable - especially considering they were missing IRB Sevens Player of the Year nominee Stefan Basson and Dubai top try scorer Danwell Demas through injury.
In the other quarter-finals, World Champs Fiji demolished Wales 33-7 while France succumbed 29-0 to the power of New Zealand.
Scotland's dismal tournament continued, going down 15-10 to Kenya in the Bowl quarter-finals.