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Springbok flank Willem Alberts's try - the only one of the match - early in the second half proved the decisive score.
But with the home side trailing 16-12 and only two minutes left, England captain Chris Robshaw - criticised for running kickable penalties during last week's defeat by Australia - told replacement flyhalf Owen Farrell to go for goal rather than opt for an attacking line-out that could have lead to a try.
International Rugby: England v South Africa Highlights
But while Farrell landed the kick, it meant England, fifth in the wold rankings, were still a point behind.
South Africa then ran down the clock to extend their unbeaten streak against England to 11 Tests.
England, who suffered a frustrating 14-14 draw with the Springboks in Port Elizabeth in June, made six changes from the side beaten 20-14 by Australia.
In the backs Mike Brown came in for left wing Charlie Sharples and Ben Youngs started at scrum-half in place of Danny Care.
Lock Joe Launchbury was given a first Test start as Wasps team-mate Tom Palmer made way and a rejigged back-row saw the return of No 8 Ben Morgan and blindside flanker Tom Wood.
Meanwhile Alex Corbisiero, fit following a knee injury, was back at loose-head prop following Joe Marler's knee injury.
South Africa, by contrast, were unchanged from the team that last week beat Scotland 21-10 at Murrayfield, having started their tour with a 16-12 win over Ireland in Dublin.
An attritional first half finished with South Africa 9-6 in front after Springbok flyhalf Pat Lambie kicked three penalties from as many attempts while his England counterpart, Toby Flood, landed two from four.
At a rainswept Twickenham, England's rejigged pack was more competitive in the scrum and loose than they had been against the Wallabies, although the Springboks had the edge in the line-out.
England lock Geoff Parling's charge-down of Springbok scrumhalf Ruan Pienaar's box-kick led to Flood's opening penalty.
But Lambie equalised soon afterwards before Flood made it 6-3 to England when Springbok tight-head prop Jannie du Plessis was penalised for not binding correctly at a scrum.
Lambie, after Robshaw broke too early from a scrum, levelled the match at 6-6 before Flood, who'd already missed one penalty, pulled his fourth effort across the posts.
South Africa, looking the more dangerous with ball in hand, went 9-6 up when, after a break by wing JP Pietersen, Lambie landed an easy penalty.
It was no surprise, given the first half, that South Africa kicked a close-range penalty to touch early in the second period and it was from the set-piece that they grabbed a try.
After a catch and drive, South Africa lost the ball but Ben Youngs's attempted fly-hack clear rebounded off Pietersen.
Wood knocked-on the loose ball and Alberts plunged over the line for a try confirmed by the television match official.
Lambie converted and South Africa were two scored ahead at 16-6.
England threatened when centre Manu Tuilagi counter-attacked from inside his own half and found Chris Ashton in support.
But Ashton's pass to fellow wing Brown was a poor one and allowed the Springbok defence time to regroup.
Just after the hour, South Africa conceded a ruck penalty and Farrell, on as a replacement for Flood, landed the 30 metre goal-kick to cut the Springboks' advantage to 16-9.
England pressed for the converted try that would have tied the scores but several knock-ons spoilt promising positions.
They clawed back some of the ground when, with eight minutes left, Farrell kicked a penalty but it was all to no avail.
Teams:
England:
15 Alex Goode, 14 Chris Ashton, 13 Manu Tuilagi, 12 Brad Barritt, 11 Mike Brown, 10 Toby Flood, 9 Ben Youngs, 7 Chris Robshaw (captain), 6 Tom Wood , 5 Geoff Parling, 4 Joe Launchbury, 3 Dan Cole, 2 Tom Youngs, 1 Alex Corbisiero
Substitutes: 16 David Paice, 17 David Wilson, 18 Mako Vunipola, 19 Mouritz Botha, 20 James Haskell , 21 Danny Care, 22 Owen Farrell, 23 Jonathan Joseph
South Africa:
15 Zane Kirchner, 14 JP Pietersen, 13 Juan de Jongh, 12 Jean de Villiers (captain), 11 Francois Hougaard, 10 Pat Lambie, 9 Ruan Pienaar, 8 Duane Vermeulen, 7 Willem Alberts, 6 Francois Louw, 5 Juandré Kruger, 4 Eben Etzebeth, 3 Jannie du Plessis, 2 Adriaan Strauss, 1 Gurthrö Steenkamp
Substitutes: 16. Schalk Brits, 17 Heinke van der Merwe, 18 Pat Cilliers, 19 Flip van der Merwe, 20 Marcell Coetzee, 21 Elton Jantjies, 22 Jaco Taute, 23 Lwazi Mvovo
