Miller entered with the tourists reeling at 58 for five at the halfway mark of the innings, though looked unfazed under pressure, combining with Wiaan Mulder (36) and the tail to add 101 runs from overs 11 to 20.
Needing eight runs an over in response, Ireland struggled to deal with the spin of Bjorn Fortuin (3/16) and Tabraiz Shamsi (3/14), who picked up three wickets each.
South Africa: 159/7 in 20 overs (David Miller 75 n.o, Paul Stirling 2/12)
Ireland: 117 in 19.3 overs (Tabraiz Shamsi 3/14). (ICC)