After a shaky start, Miller (138 not out off 92 balls) and Duminy (115 not out from 100) came together at 83-4.
They blasted the Proteas to 339-4, including 111 off the last six overs, while Miller smashed 30 off the 48th.
Hamilton Masakadza (80) helped Zimbabwe to 277 in reply, losing by 62 runs.
South Africa – three-time beaten semi-finalists – were among the pre-tournament favourites, but were less than convincing here, despite winning their 27th consecutive ODI meeting with Zimbabwe.
