Hall scored an unbeaten 67 to prop up South Africa's innings of 192 and then took three for 26 as Ireland were dismissed for 157 to lose by 35 runs.
Australian-born fast bowlers Dave Langford-Smith and Trent Johnston shared seven wickets to hold the South Africans to their mediocre total.
The Irish, who are playing in their first World Cup, bowled with penetration on a responsive pitch and fielded aggressively.
Langford-Smith dismissed Graeme Smith, AB de Villiers and Jacques Kallis cheaply before Johnston reduced South Africa to 66 for seven by removing Herschelle Gibbs, Ashwell Prince, Shaun Pollock and Loots Bosman in quick succession.
South Africa dwindled to 91 for eight before Hall and Robin Peterson rescued the innings with a partnership of 85.
Langford-Smith took three for 30 and Johnston claimed four for 40.
Ireland's reply never caught fire and their only noteworthy scores came from William Porterfield (37), Andre Botha (40) and Kevin O'Brien (33).
Fast bowler Charl Langeveldt supported Hall well to take four for 31.
