Hayden needed only 66 balls, one delivery less than Canadian John Davison's effort against West Indies in 2003, to reach his century before he was caught for 101.
Captain Ricky Ponting scored 91 and Michael Clarke 92 in Australia's 377 for six, their highest World Cup total.
South Africa captain Graeme Smith and AB de Villiers put on 160 for the first wicket but after de Villiers was brilliantly run out by Shane Watson for 92 the innings lost momentum.
Smith, who was forced to retire hurt with cramp after scoring 72, added only two more on his return before he was caught and the innings finally closed on 294 with two overs to spare.
The win allowed Australia to carry two points into the Super Eights starting next week.
Adam Gilchrist and Hayden tore into the South African bowling, and Australia reached 100 off 81 balls when Hayden drove medium pacer Andrew Hall over extra cover for six.
Fast bowler Charl Langeveldt separated the openers in the 15th over with 106 runs on the board. Gilchrist fell for 42 after steering a mistimed cut to Herschelle Gibbs at backward point.
Hayden claimed his record in the 23rd over with a straight six off part-time off-spinner Graeme Smith.
The strapping left-hander was dismissed seven balls later when he looped a delivery from fast bowler Jacques Kallis to Gibbs at backward point.
Hayden faced 68 balls in all and hit 14 fours and four sixes in his chanceless innings.
Ricky Ponting and Michael Clarke ensured that Australia maintained the pace with a brisk stand of 161 for the third wicket.
Ponting scored a run-a-ball 91 while Michael Clarke hit 92 off 75 balls.
Clarke was dropped on eight by De Villiers at short mid-wicket and again on 56 by Gibbs.
Pollock's figures of nought for 83 were his worst in his 277 one-day internationals.
Smith and De Villiers kickstarted South Africa's reply with a free flowing partnership. None of Australia's bowlers threatened the openers, and it was left to Watson to end the stand with a stunning direct hit from the backward square leg boundary to run out De Villiers for 92 in the 21st over.
Smith retired hurt with cramp on 72 in the 26th over, and leg spinner Brad Hogg soon had a lunging Gibbs stumped for 17 by wicketkeeper Gilchrist.
Five balls later Ashwell Prince was out for one when he pulled a Glenn McGrath delivery and was caught by Hayden at deep square leg.
The South Africans' last real hope was snuffed out in the 41st over when the returning Smith faced just two more balls before he miscued a sweep off Hogg and was caught by Gilchrist for 74.
Hogg took three for 61.