The left-handed duo of Miller (138* off 92 balls) and Duminy (115* off 100) lifted South Africa to 339 after struggling at 83 for four. In the process, the two shared a world record fifth-wicket partnership with an unbeaten 265-run stand off 178 balls.
Zimbabwe gave their best during the steep chase but a middle-order collapse led to their downfall and they ended at 277 with 10 balls to spare. The contributions from Chamu Chibhabha (64), Hamilton Masakadza (80) and Brendon Taylor (40) went in vain.
South Africa's premier pace bowler Dale Steyn had a not-so-good day in office, conceding 48 runs in eight overs. Leg-spinner Imran Tahir was the pick of the bowlers, taking three wickets for 36 runs in 10 overs.
Earlier, Miller and Duminy led South Africa's recovery after Zimbabwe bowled well on a pitch offering assistance to the fast bowlers.
A big upset looked on the cards when Zimbabwe had their fancied rivals reeling at 83 for four with their in-form skipper Ab de Villiers (25) also back in the hut. It was a moment to remember South Africa's shock loss against their African counterparts in the tournament's 1999 edition.