England had collapsed to 79 for four, needing a further 395 runs to reach their victory target of 474, at lunch on the fourth day of the second Test against South Africa at Trent Bridge on Monday.
Jonny Bairstow was 12 not out and Ben Stokes five not out.
Vernon Philander (two for 16 in seven overs) and Chris Morris (two for seven in six) had removed all of England's top four between them in Monday's first session.
The most any side have made to win in the fourth innings of a Test is the West Indies' 418 for seven against Australia at St John's, Antigua, in 2002/03.
England lead this four-match series 1-0 after a 211-run win in the first Test at Lord's.