With no prospect of forcing a result to level the three-match series, New Zealand were 121 for three in their second innings when bad light ended the match.
Prince batted patiently on a pitch which again offered no help to the bowlers. It took him almost two hours to move from his overnight score of 70 to his fourth Test hundred, which he reached with a straight drive for four off New Zealand left-arm bowler James Franklin.
He had faced 259 balls and hit nine fours. The South African innings ended shortly after lunch.
New Zealand's opening batsmen again looked shaky against South Africa's new ball pair of Dale Steyn and Makhaya Ntini.
Steyn had Michael Papps caught at the finer of two gullies for 20 and Ntini had Peter Fulton caught at second slip for 11.
Man-of-the-Match Stephen Fleming, who scored 262 in the first innings, did not bat in the second innings. Scott Styris, who scored 30 runs in his first three innings in the series, batted in Fleming's usual place at number three and made an unbeaten 54.
Nathan Astle was out for 14 when he was caught at cover off Jacques Kallis.
The match yielded 1226 runs for the loss of only 21 wickets after South African captain Graeme Smith gambled by sending New Zealand in.
There was brief excitement at the start of the final day when Franklin, who made a century batting at number nine in New Zealand's first innings, struck twice in two balls in the fourth over of the day after South Africa resumed at 427 for five.
Mark Boucher was caught by Fleming at first slip for 33 when he top-edged a pull and Fleming jumped to catch the ball above his head.
The left-handed Nicky Boje was leg before wicket next ball, going back on his stumps and being struck low down by a ball that swung in to him.
Boje batted with his right hand strapped after having five stitches in the webbing between thumb and forefinger.
He bowled in the second innings and selection convenor Haroon Lorgat said he had not been ruled out of playing in the third and final Test starting in Johannesburg on Friday.
Andre Nel survived the hat trick ball and batted for over an hour before falling to Franklin after the second new ball was taken. Franklin made the first ball of his second spell swing in and Nel was leg before for 12. Franklin took three for 95.
Left-arm spinner Daniel Vettori claimed his second wicket of the innings when Steyn was stumped. It was Vettori's 218th Test wicket for New Zealand, putting him joint second with Chris Cairns on the country's all-time list, behind Richard Hadlee, who took 431.
South Africa won the first Test at Centurion by 128 runs.
Scoreboard
NEW ZEALAND (1st Innings) 593-8 declared (S.P. Fleming 262, J.E.C. Franklin 122 not out, N.J. Astle 50; M. Ntini 4-162).
SOUTH AFRICA (1st Innings, overnight 427-5):
G.C. Smith c and b Patel 25
H.H. Dippenaar b Patel 47
H.M. Amla lbw b Vettori 149
J.H. Kallis c Martin b Oram 71
A.G. Prince not out 108
A.B. de Villiers c Papps b Patel 13
M.V. Boucher c Fleming b Franklin 33
N. Boje lbw b Franklin 0
A. Nel lbw b Franklin 12
D.W. Steyn st McCullum b Vettori 13
M. Ntini run out 11
EXTRAS (B-15, LB-10, NB-5) 30
TOTAL (all out, 188 overs) 512
FALL OF WKTS: 1-36, 2-108, 3-252, 4-344, 5-361, 6-435, 7-435, 8-462, 9-495.
BOWLING: Martin 20-7-62-0; Franklin 33-5-95-3 (1nb); Vettori 63-10-147-2 (2nb); Patel 42-8-117-3 (1nb); Styris 10-2-33-0 (1nb); Oram 18-10-24-1; Astle 2-0-9-0.
NEW ZEALAND (2nd Innings):
M.H.W. Papps c Prince b Steyn 20
P.G. Fulton c Kallis b Ntini 11
S.B. Styris not out 54
N.J. Astle c Smith b Kallis 14
J.D.P. Oram not out 8
EXTRAS (LB-10, NB-4) 14
TOTAL (for three wkts, 37 overs) 121
FALL OF WKTS: 1-34, 2-41, 3-81.
BOWLING: Steyn 9-3-26-1 (3nb); Ntini 8-2-25-1 (1nb); Nel 10-2-41-0; Kallis 5-3-5-1; Boje 5-1-14-0.
UMPIRES: M.R. Benson (England) and E.A.R. de Silva (Sri Lanka).
TV UMPIRE: M. Erasmus (South Africa).
MATCH REFEREE: R.S. Madugalle (Sri Lanka).
MAN-OF-THE-MATCH: Stephen Fleming.
FIRST TEST: Centurion, South Africa won by 128 runs.
THIRD TEST: Johannesburg, May 5-9.—Agencies