The home side were 457 runs behind with nine wickets in hand when bad light stopped play for the day.
Captain Chris Gayle [ Images ] led the run chase with an unbeaten 42 while Narsingh Deonarine, promoted to the number three position ahead of Brendan Nash [ Images ] who occupied that position in the previous Test, was the other not-out batsman on 33.
After opener Travis Dowlin was caught by AB de Villiers [ Images ] at slip for 10 off a Morne Morkel [ Images ] delivery, Gayle and Deonarine combined for 73 runs as Gayle plastered seven fours and Deonarine hit two fours and a six.
De Villiers hit 13 fours and six sixes from 168 balls to help him reach 135.
South Africa won the first Test by 163 runs.
South Africa (1st innings):
G Smith b Roach 132
A Petersen c Roach b Shillingford 52
H Amla c Bravo b Shillingford 44
J Kallis c Rampaul b Shillingford 110
AB de Villiers not out 135
A Prince c Gayle b Benn 9
M Boucher run out 17
D Steyn not out 20
Extras: (lb-5, w-2, nb-17) 24
Total: (for 6 wickets - declared) 543
Did not bat: P. Harris, M. Morkel, L. Tsotsobe
Fall of wickets: 1-99, 2-211, 3-283, 4-421, 5-442, 6-490.
Bowling: K. Roach 22-4-72-1 (nb-12 w-1), R. Rampaul 18-4-65-0 (nb-1), S. Benn 30-3-124-1, D. Bravo 18-2-58-0 (w-1), S. Shillingford 52-4-193-3 (nb-4), N. Deonarine 3-0-20-0, B. Nash 4-0-6-0
West Indies (1st innings):
C Gayle not out 42
T Dowlin c de Villiers b Morkel 10
N. Deonarine not out 33
Extras: (nb-1) 1
Total: (for 1 wicket) 86
Fall of wickets: 1-13
Bowling: D. Steyn 7.2-2-15-0, M. Morkel 6-0-29-1 (nb-1), L. Tsotsobe 4-0-19-0, P. Harris 6-0-23-0.