Amla was unbeaten on 63 with Petersen on 34 as the New Zealand bowlers failed to fire on a green-tinged wicket under heavy cloud cover.
Play was delayed for three-and-a-half hours following heavy rain in Wellington, and with conditions ripe for bowling, New Zealand captain Ross Taylor had no hesitation in putting South Africa in to bat.
But New Zealand quicks Chris Martin, Doug Bracewell and Mark Gillespie lacked penetration, leaving Taylor to call on spinner Daniel Vettori and part-timer Dean Brownlie, whose two overs cost 20 runs.
South Africa could consider themselves unlucky to lose the one wicket to fall, skipper Graeme Smith, who was caught behind by Kruger van Wyk off the bowling of Bracewell for five.
Smith appealed against the decision and television replays were inconclusive with a clear sound as the ball passed the bat but no touch registered with the hotspot detector.
Brownlie was brought into the side at the expense of bowler Brent Arnel to bolster the batting line-up after New Zealand failed to make 200 in either innings of the second Test, where they were beaten by nine wickets.
The other change to the New Zealand side is at the top of the order, where in-form Daniel Flynn was recalled to open the innings at the expense of Rob Nicol.
South Africa reacted to the Wellington conditions by strengthening their pace attack with Marchant de Lange replacing spinner Imran Tahir.
The other change in the tourists' line-up is the inclusion of JP Duminy, who replaces Jacques Kallis, unavailable with a stiff neck.