Hayden hit his 100 off just 66 balls while Michael Clarke (92) and skipper Ricky Ponting (91) joined the run feast as Australia piled up their highest World Cup score of 377-6 after being put in to bat.
South Africa were cruising along at 184-1 in reply after 25 overs on the back of a robust opening stand of 160 between captain Graeme Smith (74) and AB de Villiers (92) before they were bowled out for 294 in 48 overs.
The win gave two extra points to the defending champions in the next round Super Eights and extra confidence in their bid to achieve hat-trick of World Cup titles.
Smith and De Villiers gave the Australian bowlers no respite before they collapsed to lose their last nine wickets for 74 runs.
De Villiers showed his intentions by sending Nathan Bracken's fourth ball of the innings to the ropes before going on to complete his half-century off 47 deliveries.
The 23-year-old De Villiers hit three successive boundaries off Andrew Symonds before failing to beat Clarke's dire