But England failed to add to that tally after the break apart from a Rory Clegg penalty with the Springboks turning the game on its head thanks to tries from Patrick Lambie and Sibusio Sithole.
Although they piled on the pressure in the closing stages, it could not stop England's tournament ending a disappointing note following two consecutive second place finishes.
France claimed fifth with a gutsy 37-23 win over hosts Argentina as flanker Kevin Gimeno bagged two tries.
Captain Mickael Ivaldi, Romain Taofifenua and Brice Dulin were also try-scorers to clinch the hard-fought win.
Two tries from Morgan Allen and 22 points from the boot of Matthew Jarvis helped Wales clinch seventh place with a 39-15 win over Fiji.
Centre Navitalai Ratulevu gave Fiji the lead but four penalties from Jarvis edged Wales 12-10 in front at the break.
And after the restart Allen and Gareth Davies scored tries to clinch the win on the back of a dominant performance from the pack.
Full-back Andrew Conway bagged a brilliant hat-trick as Ireland saw off RBS 6 Nations rivals Scotland 53-23 to finish in ninth place.
Allen Clarke's side ran riot with seven tries in as half-backs Noel Reid, who finished with 20 points, and John Cooney, captain Niall Annett and winger Simon Zebo also went over.
Robert Harley and Stuart McInally scored Scotland's two tries but they had no answer to the Irish's attacking prowess.
New Zealand retained their crown with a 62-17 destruction of Australia in the final thanks to a hat-trick from Baby Blacks winger Telusa Veainu.