Johannesburg - Proteas coach Mark Boucher insisted his weary team "have to hold on to some positivity" despite being handed a world record target of 466 to win the fourth and final Test against England at the Wanderers.
With two days left in the match, England are comfortably placed to complete a 3-1 series triumph.
"If you look at the amount of time left in the game we've still got to look at going for a win," said Boucher.
"It's never been done before but we have to hold on to some positivity."
Boucher admitted, however, that it had been a tough series for a largely inexperienced team.
"But that's what Test cricket is all about. It's about going through tough times and stepping up when required."
Joe Root made a patient 58 and played an anchor role before he was last man out as England were bowled out shortly before the close for 248 in their second innings.
The England skipper had decided not to enforce the follow despite England leading by 217 runs on first innings.
Fast bowler Mark Wood took five for 46 as South Africa were dismissed for 183.
Quinton de Kock (76) and Dwaine Pretorius (37) put on 79 for the eighth wicket and prevented England from wrapping up the innings early.
De Kock scored his fourth half-century of what has been a poor series for the South African batsmen.
His team-mates have contributed only five other 50-plus scores between them.
When England batted again, left-arm seam bowler Beuran Hendricks claimed five for 64 in what Boucher described as an improved bowling performance in the second innings.
"You saw in the field today the guys tried really hard," said Boucher. "We've got the fight back."
Ben Stokes, Sam Curran and Mark Wood all batted with freedom as England stretched their lead despite losing wickets at regular intervals.
South Africa were without Vernon Philander, their leading bowler, for most of the innings.
It was an unhappy day for Philander, who will be retiring from international cricket at the end of the match.
He was out for four to the sixth ball of the day when the follow-on seemed a strong possibility.
He also received a fine of 15 percent of his match fee for his 'send-off' of Jos Buttler on the second day and then pulled up with a hamstring injury after bowling just nine balls in the second innings.
He left the field immediately and was sent for a scan.
Boucher said Philander had a grade two tear but that he was likely to bat.
"I'm sure that Vern in his last innings will definitely go out and bat and try and add value to the team," he said.
England all-rounder Sam Curran said his team were confident that they could complete a 3-1 series win.
"The wicket will assist us, especially in terms of the carry, we know the edges will carry to the slips," said Curran.
England will look to repeat what Curran said was a "great bowling performance in the first innings," in which fast bowler Mark Wood took five for 46.
"Mark brings so much energy," he said.
Wood also has the ability to bowl at 150kmh on a pitch which provides encouragement to pace bowlers and which showed signs of uneven bounce on Sunday.