New Zealand, who had looked in danger of handing the game to South Africa at 111 for five, had a lead of 109 when bad light stopped play five overs early.
The home team began their second innings with a 19-run deficit after South Africa collapsed in their first innings to 316.
New Zealand seamer Chris Martin followed up his 11 wickets in the second Test with a five-wicket haul as the tourists, resuming at 237 for three, lost their last seven wickets for the addition of 79 runs. Overnight batsman Jacques Rudolph was left stranded on 93 not out.
Martin put his success down to some tentative South African batting.
"They were a wee bit on edge, I suppose, and that helps when you get an early wicket and the team gets behind you," Martin said. "We put the willies up them a bit and they didn't like it."
EVENLY POISED
But South Africa made up for their poor batting display by comfortably dispensing with New Zealand's top order.
"We let ourselves down in the morning today," South African captain Graeme Smith said. "I had different plans for the day but we failed with the bat and now things are fairly evenly poised."
"The bowlers have been superb. We've built some serious pressure and we've got wickets at crucial times, but there are still five big ones to go tomorrow."
Michael Papps was the first New Zealand wicket to fall, trapped lbw for a duck by Shaun Pollock in the opening over.
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Mathew Sinclair (21) was lbw to Pollock without offering a stroke and Mark Richardson, who had made a painstaking 37 off 142 balls, attempted to lift Nicky Boje over mid-wicket but hit the ball straight to Smith.
Brendon McCullum was then bowled for three attempting to sweep Boje.
Earlier, Martin had struck with the new ball to have Martin van Jaarsveld caught by Jacob Oram in the gully for 59.
The batsman of the series, Jacques Kallis, then edged a ball from Martin to wicketkeeper McCullum for a duck.
In the same over, Boucher nicked Martin to Papps at third slip for another duck. Martin finished with five for 55.
Pollock was the next victim, caught by Fleming at first slip off Oram for five.
Boje (25) was bowled by Cairns and Ntini fell for four when he ducked a bouncer, the ball struck his bat and ballooned high for McCullum to catch.
Cairns made it three wickets in eight balls when last man Nel was snapped up in the gully by Oram for a duck.
New Zealand lead the series 1-0.
Scorecard:
New Zealand first innings 297
Second innings
M.Papps lbw b Pollock 0
M.Richardson c Smith b Boje 37
S.Fleming c Boucher b Nel 9
M.Sinclair lbw b Pollock 21
S.Styris not out 41
B.McCullum b Boje 3
C.Cairns not out 7
Extras (lb-4 b-1 w-2 nb-3) 10
Total (for five wickets) 128
Fall of wickets: 1-1, 2-42, 3-73, 4-107, 5-111
Bowling: Pollock 15-9-31-2 (w-1 nb-3), Ntini 11.4-3-28-0 (w-1), Nel 12-4-24-1, Boje 21-6-40-2
South Africa first innings
G.Smith b Cairns 47
H.Gibbs c sub b Martin 77
J.Rudolph not out 93
G.Kirsten c McCullum b Martin 1
M.van Jaarsveld c Oram b Martin 59
J.Kallis c McCullum b Martin 0
M.Boucher c Papps b Martin 0
S.Pollock c Fleming b Oram 5
N.Boje b Cairns 25
M.Ntini c McCullum b Cairns 4
A.Nel c Oram b Cairns 0
Extras (nb-4 lb-1) 5
Total (all out) 316
Fall of wickets: 1-103, 2-130, 3-136, 4-251, 5-265, 6-265, 7-270, 8-304, 9-308
Bowling: Martin 20-6-55-5 (nb-2), Mason 16-4-73-0, Oram 11-3-21-1, Vettori 26-6-76-0, Cairns 16.5-2-60-4 (nb-2), Styris 10-4-30-0
