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England played the better wet-weather rugby as they forced the Springboks, who ended up winning the series 2-1, into numerous errors with the platform for victory laid by a 14-6 penalty count in their favour.
Wing Jonny May also added a late try, superbly set up by a kick from flyhalf Danny Cipriani, who was making his first start for England in a decade but had little other influence on the game in the difficult conditions.
The only try for the Boks came from centre Jesse Kriel as the home side, who made five changes for the test, battled to breach a resolute England defence.
The conditions suited the visitors and they maximised that advantage with a more intelligent and accurate kicking game with ball in hand.
After Bok flyhalf Elton Jantjies, who had a poor game in the place of the rested Handre Pollard, had missed an early penalty, Farrell booted England ahead on 10 minutes.
It took until 37 minutes for the next score as South Africa were penalised for slowing down the play at the ruck after Jantjies had dropped the ball to put his side under pressure deep in their own half and Farrell landed the simple kick.
The Boks were on the board with the last play of the first half when Jantjies kicked a penalty after the hooter as England transgressed at the ruck and the visitors led 6-3 at the break.
England won a scrum penalty early in the second period, again after Jantjies had dropped the ball, that was converted by Farrell.
The first try of the game was scored by the Boks soon afterwards in a move started and finished by Kriel.
He found the slightest of gaps in the visitors’ defence out wide and tore into the England 22. Fullback Warrick Gelant then supplied a clever grubber kick and Kriel was able to gather over the line.
Jantjies slotted home a difficult conversion effort and the Boks had a lead of one, though it was short-lived.
Gelant immediately entered the ruck from the side and provided a penalty chance for Farrell, who slotted home to take England ahead again.
With the penalty count mounting against the Boks, Farrell extended the lead to five points and victory was sealed when Cipriani’s excellent cross-field kick into the corner of the Bok goal-line was dotted down by May.
It was England's first test try against South Africa at Newlands in their third appearance in Cape Town and eased the pressure on coach Eddie Jones as the tourists came away with some consolation from a difficult tour.