The tourists were bowled out for 83 in 23 overs and England chased down their target with 35.5 overs to spare to take a 2-0 lead in the five-match series.
Matt Prior (45 not out) and Ian Bell (28 not out ) knocked the runs off with the minimum of fuss as England recorded a ten wicket win for only the third time in one-dayers.
Prior also equalled the world record for the number of dismissals in an innings claiming six catches as South Africa tumbled to their lowest ever one-day score against England and the second lowest in their history.
Prior joins Adam Gilchrist, Alec Stewart and Mark Boucher as the only wicket-keepers to take six catches in an innings in a one-day international.
The South African batsmen looked disinterested at the end of a long tour as Broad and Andrew Flintoff, who took three for 25, used their height and bounce to reduce South Africa to 53 for seven.
The highest scorer was Andre Nel, coming in at number nine, who slogged three boundaries, and only two of the top six made it to double figures.
Broad's figures comfortably eclipse his previous best of four for 51 which he took against India at Old Trafford last year.
If it had not been for Nel's cameo South Africa would have been in danger of recording the lowest score in their one-day international history but the all-rounder got them past the 69 they made against Australia at Sydney in 1993.
Their previous lowest against England was the 107 they scored in the triangular series final at Lord's in 2003.
On his home ground Broad, 22, kicked off with the wicket of Herschelle Gibbs who edged a lifting delivery to give keeper Prior the first of his six catches and also dismissed Graeme Smith also with Prior's assistance.
By now Broad had his tail up and induced an edge from Jacques Kallis which Owais Shah took comfortably.
J-P Duminy edged another one to Prior to give Broad his fourth wicket and the South Africans then had to contend with Flintoff who replaced the wicketless James Anderson in the 11th over.
The big all-rounder soon had AB de Villiers leg for five and Mark Boucher caught behind and Harmison was not introduced until the 22nd over.
As is the way with Kevin Pietersen's captaincy at the moment Harmison got a wicket with his first ball as Andre Nel slogged him high up in the air to Luke Wright at mid-on.