The left-handed Miller made 130 not out in a total of 262 for eight in Port Elizabeth.
Miller came in with his side struggling at 32 for three in the seventh over. It became 76 for four when captain AB de Villiers was out for 19.
JP Duminy helped Miller add 90 for the fifth wicket but it was hard going for South Africa against a much-improved West Indian bowling performance on a slow pitch which offered some seam movement.
Left-arm fast bowler Sheldon Cottrell, making his one-day international debut, took two for 30 in an aggressive opening spell, dismissing opening batsmen Rilee Rossouw, superbly caught at second slip by Darren Sammy for four, and Morne van Wyk, caught behind for 18.
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