In a match reduced to 34 overs a side, the pair put on 51 off 23 deliveries as New Zealand posted 207 for seven.
They were particularly harsh on the most successful of the South African bowlers, Chris Morris, smacking the all-rounder for 25 in the final over of the innings.
It saw Morris's figures balloon out to four for 62 off his seven overs, after he had four for 24 off five.
In his first three-over spell, Morris took one for 18. When he returned for his second spell he took three for six in two overs and then he was hammered by de Grandhomme and Southee in his final outing.
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De Grandhomme was unbeaten on 34 off 19 balls while Southee faced 13 balls to be 24 not out.
It was a bright end after a dismal start for New Zealand, when Tom Latham was lbw to Morris without scoring for his second consecutive duck. It continued an unproductive run in ODIs, where he has totalled just 33 in his past five innings.
Ross Taylor was caught and bowled for one and Neil Broom (two) went in similar fashion to Brownlie as New Zealand tumbled from one for 69 to four for 82.
Williamson reached his 28th ODI half century with ease before he misread a turning Tabraiz Shamsi delivery.
Jimmy Neesham added a cautious 29 and Mitchell Santner 17 as the run rate slowed before the final onslaught by de Grandhomme and Southee gave New Zealand a competitive score.
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