Having lost five of their last six Tests, England crucially needed to get their campaign off to a positive start at Twickenham this afternoon.
Despite being dominated in the first half, they came back brilliantly in the second period and Farrell, in his first game as co-captain with Dylan Hartley, remained cool to slot a difficult 73rd minute penalty from wide out to put them ahead.
However, in the final seconds, with some players already celebrating after the ball had gone out of play, referee Angus Gardner called on the TMO to check a Farrell tackle on Andre Esterhuizen which appeared to be made with no arm contact wrapped around.
The incident had occurred within kicking distance for Handre Pollard, who was left with his head in his hands after an earlier long-range penalty had shaved a post five minutes from time.
However, to some surprise, the officials deemed Farrell's tackle was legitimate and, after a brief word from the referee, the elated England fly-half wheeled away to celebrate a famous win ahead of New Zealand's visit next Saturday.
His own penalty had come after his pack had forced a penalty on South Africa’s 5m scrum.
It was fitting the victory came in that fashion; the Springboks had utterly dominated that set-piece in the first half, realising England were bereft of so many stellar front-line operators.
It was no surprise, then, when Jones’ side celebrated when - with Exeter prop Ben Moon on for his debut - they making the South African scrum crumble to their knees.
England had shown their spirit was in tact by coping handsomely with the loss of Maro Itoje to a 16th minute yellow-card, the British Lion lock having been offside when snaffling Ivan van Zyl just as the Springboks scrum-half looked set to burrow over.
Not only did they protect their line in the ensuing 10 minutes but, with the first of Farrell’s three penalties, they also levelled the game at 3-3.
Still, how England were just 8-6 behind at half-time is anyone’s guess given they were dominated in all areas by their opponents.
But, on a November day where sunglasses were need at kick-off rather than thermals, maybe everything was upside down.
The Springboks were restricted to just one try, a slick effort to expose England’s left channel with No8 Warren Whiteley, in particular, showing real class with his sharp, deft pass for winger Sibusiso Nkosi to scamper over in the 33rd minute.
It had been coming; England, twice shoved off their own scrum, struggled to get out of their own half for much of the period and Damian de Allende, the stylish centre, caused them all sorts of problems in midfield with his piercing angles.
So, too, did Eden Etzebeth, although the stellar lock was more trouble due to his thunderous carriers rather than any sort of guile.
However, fortunately for England, the visitors had some issues of their own; hooker Malcolm Marx twice missed his jumper to waste promising attacking positions while Handre Pollard - otherwise classy at No10 - threw one wild pass that Henry Slade almost intercepted.
It meant, despite never once having any possession in the Springboks’ 22 in the opening 40 minutes, Owen Farrell’s two penalties kept them in touching distance.
Jones made a change at the interval, bringing on Exeter prop Ben Moon for his debut in place of club-mate Alec Hepburn, to try and sort the scrum issue.
It did improve things. Furthermore, though, within 90 seconds of the second period, the visitors saw talisman Etzebeth limp off.
Granted, England lost openside Tom Curry to an injury at the same time but it was the Springboks who were unsettled most.
Marx was wayward with yet another line-out throw and the home side enjoyed some positive moments in attack, not least when tighthead Kyle Sinckler fired out a fine pass that Farrell would have been pleased with him himself.
Elliot Daly found space, Farrell started to work some openings in the middle and Daly was able to strike a long-range penalty in the 51st minute to suddenly give his side the lead.
Farrell was off-target with another effort which meant the visitors regained the lead when George Kruis was penalised for not releasing in the 68th minute.
May wasted a glorious chance with an awful forward pass to Brad Shields soon after but it mattered not as, from the following scrum, came that turning point.
Danny Care produced a try-saving tackle on de Allende before the late drama at the death.
England: Daly; Nowell (Ashton 65), Slade, Te’o (Ford 72), May; Farrell, Youngs (Care 65); Hepburn (Moon 40), Hartley (George 57), Sinckler (Williams 65), Itoje, Kruis, Shields (Ewels 77), Curry (Mercer 41), Wilson.
South Africa: Willemse; Nkosi (Esterhuizen 60), Kriel, de Allende, Dyantyi; Pollard, van Zyl (Papier 75); Kitshoff, Marx (Mbonambi 74), Malherbe (Louw 65). Etzebeth (Snyman 42), P du Toit, Kolisi (de Jager 65), Vermeulen, Whiteley.
Referee: Angus Gardner (ARU)