Quinton de Kock's game-changing partnership with Temba Bavuma left the Proteas feeling comfortable with an 81-run lead after day two of the second Test against New Zealand in Wellington on Friday.
The value of their stand was enhanced by the last wicket pair of Vernon Philander (36*) and Morne Morkel (31*), who added 47.
De Kock top-scored with a free-flowing 91 (118 balls, 10 fours, 3 sixes), while Bavuma recorded his highest score since his maiden century against England at Cape Town a year ago after making an invaluable 89 (160 balls, 9 fours).
With de Kock on 63 and Bavuma on 61, the tourists need a further 51 runs to overhaul New Zealand's 268.
Medium-pacer Colin de Grandhomme had put New Zealand on top before lunch with the key wickets of Hashim Amla for 21 and Faf du Plessis for 23.
Matt Henry looms as the most likely third seaming option for the hosts along with Southee and Neil Wagner, with the wicket at the Basin Reserve offering a green tinge on Wednesday after several days of heavy rain and inclement weather in Wellington.
De Kock was the more aggressive of the two, hitting 91 off 118 balls, including 10 fours and three sixes, and was on course for a fourth Test hundred until he was caught behind off Jimmy Neesham.
The Proteas ended the day at 349-9 with Philander 36 not out and Morkel 31, approaching his highest Test score of 40. Southerly winds are set to pick up on Saturday, which will make bowling tough for South Africa, and if New Zealand can make sure they set a decent target, Wagner hopes Patel can still have a say - if not on de Kock, then on the outcome of the match.
The first session belonged to New Zealand as it claimed four wickets to reduce South Africa from 24-2 at the resumption to 104-6.
"He's fine‚" De Kock said of Morkel's recovery from the blow.
The second session featured a continuation of the developing rivalry between de Kock and New Zealand off-spinner Jeetan Patel.
"Credit to them, they played really well and the wicket's flattened out a lot".
The loss of Taylor means captain Kane Williamson is New Zealand's sole batting figurehead and "if we get through him we can put some real pressure on their batters".
It will be Broom's Test debut but he has played 30 one-dayers including three in the recent series against South Africa where he had scores of two, two and a duck.
Bavuma had a let-off on five when he skied a Wagner bouncer and de Grandhomme slipped when moving to take what should have been a regulation catch.