Adam Milne talks to Radio Sport's the Crowd Goes Wild Breakfast
Steyn, Vernon Philander, David Wiese and Imran Tahir all took two wickets each for South Africa.
South Africa's victory, which was some form of revenge for losing to New Zealand in the semifinals of this year's World Cup, was set up by Amla, though.
His innings, with 13 fours and three sixes, took him level with Herschelle Gibbs for the most centuries for South Africa in ODIs. Amla was supported by 89 from Rilee Rossouw as the pair put on 185 in their second-wicket partnership, taking the hosts from 46-1 off 8.4 overs to 231-2 off 41.5 overs.
Opener Tom Latham hit 60 for the Black Caps, and captain Kane Williamson added 47 for a strong start. But New Zealand played some rash shots in the middle order, when batsmen were set for larger scores, to surrender the advantage.
Nathan McCullum was out for 10 to a running, diving catch by Farhaan Behardien on the square leg boundary.
James Neesham and McClenaghan hit some late boundaries, but Steyn and then a run out created by Vernon Philander finished it off.
The second game is in Potchefstroom on Sunday.