Southee had Stephen Cook caught at second slip by Jimmy Neesham for three before de Grandhomme, a surprising choice to share the new ball, had Dean Elgar also snapped up by the same fielder for nine to reduce the Proteas to 12 for two.
Nightwatchman Kagiso Rabada was on eight with Hashim Amla yet to score at the close after the hosts had earlier been bolstered by Henry Nicholls' maiden test century of 118.
Nicholls combined for 116 runs with BJ Watling (34) for the sixth wicket after the hosts had been reduced to 21 for three in the 11th over and then 73 for four at lunch.
Nicholls combined with opener Jeet Raval for 52 after New Zealand struggled after being asked to bat by Faf du Plessis. He brought up his milestone when he hooked a Rabada delivery to the mid-wicket fence.
The 25-year-old, who chopped a delivery onto his stumps on 98 against Bangladesh in January, raised his arms in the air before the ball crossed the rope for his 12th boundary.
Nicholls and Watling's partnership, built on rotating the strike with quick singles, halted the early momentum South Africa had built in the first session through their pace attack of Morne Morkel, Vernon Philander and Rabada.
Rabada captured two wickets, including that of New Zealand captain Kane Williamson (two), whom du Plessis had targeted as the key to exposing a raw batting line-up shorn of the injured Ross Taylor.
Neil Broom lasted just four balls on debut when a Rabada delivery squared him up and caught the outside edge of the bat.
Jimmy Neesham was the only wicket to fall in the middle session for 15, before Nicholls's dismissal sparked a collapse of three wickets for five runs after tea with part-time off-spinner JP Duminy capturing all three.
Jeetan Patel and Southee then blasted a quickfire 44 runs before Morkel dismissed Southee for 27 then Duminy captured the final wicket of Neil Wagner for two to wrap up the innings and finish with 4-47.
(Reporting by Greg Stutchbury; Editing by Sudipto Ganguly)
