New Zealand were 15 for two, 248 runs behind South Africa's first innings total of 263, when play ended for the day.
Steyn, who had failed to complete the only two Tests he had played in South Africa's last eight matches because of groin and shoulder injuries, had Tom Latham caught at first slip by Hashim Amla for four off the second ball of his fourth over.
Steyn took two wickets for three runs in six overs.
Latham added only one run after being dropped off Vernon Philander, also returning from injury.
Guptill survived an appeal for leg before wicket off Steyn's fourth ball of the innings when he was on two.
Umpire Richard Illingworth turned down the appeal and South Africa decided not to ask for a review. Replays showed the ball was clipping leg stump in the 'umpire's call' area so a review would have failed.
Although Steyn had the better figures, Philander also looked close to his best form after missing South Africa's most recent seven Test matches because of an ankle injury.
In the last over before lunch he twice beat Ross Taylor with balls that swung sharply away from the bat.
It took New Zealand ten overs to take South Africa's remaining two wickets after rain delayed the start by 50 minutes.
Tim Southee struck with the eighth ball of the day when he bowled Steyn before South Africa had added to their overnight total of 236 for eight.
Rabada, who was dropped by Southee at third slip off Boult when he had 16, battled his way to an unbeaten 32 before Piedt was last man out, caught behind off Boult for nine.
Boult finished with figures of three for 52.
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