Play had begun nicely poised at The Oval but Flintoff's heavy bat and Harmison's pace and steepling bounce left England in sight of victory at the end of a dramatic fourth day.
South Africa, 2-1 up and seeking their first series win in England since 1965, ended on 185 for six in their second innings, 65 ahead, with Mark Boucher and Shaun Pollock at the crease.
Michael Vaughan's side, however, will be well aware of their opponents' resilient batting.
The home team had resumed their first innings on 502 for seven, 18 runs ahead, and lost a wicket to Pollock's third delivery of the day.
Flintoff, however, conjured up perhaps the most important, and certainly most intelligent, innings of his career, hammering 95 runs and putting on 99 for the ninth wicket to take his side to an improbable 604 for nine declared, 120 ahead.
His partner, the studious Harmison, contributed three to their stand before Flintoff attempted a second six off Paul Adams's wrist spin and lost his leg bail after a 104-ball stay.
None of the bowlers had been safe -- four South Africans conceded more than 100 runs in the innings -- as Flintoff, a brash man with a big smile, heaved boundaries early in each over before protecting Harmison from the strike with singles. Flintoff drove, pulled and hoiked five fours and a six off Jacques Kallis's first five overs of the day, enjoying an exchange of words with the South African in the process.
Strike bowler Makhaya Ntini, unable to locate his yorker, was hooked and driven for consecutive sixes as his three overs went for 31.
Flintoff hit 27 off 11 balls on the way to his 50 before falling just short of a third Test century.
His innings, taking his series average past 50 and hugely appreciated by a sell-out crowd, transformed England's mood.
They had moped about on the way to defeat in the fourth Test but this time there was a spring in the step as South Africa batted again.
Soon Herschelle Gibbs chased a wide James Anderson half-volley and edged behind with 24 on the board and skipper Graeme Smith -- 714 runs in the series, average 79.33 -- soon followed.
PLAYED BACK
Lucky to escape an early lbw shout and a millimetre away from stepping into his own stumps as he played back to Anderson, he was trapped in front for 19 by a Martin Bicknell inswinger.
Harmison, as imposing a figure as the giant Flintoff but of a more demure character, then made his second major contribution as he took two wickets in four balls without conceding a run.
Gary Kirsten, the innings anchor, snicked him to first slip for 29 and Kallis went lbw for 35 as he was trapped on the back foot to make it 93 for four.
Harmison, in his best spell of the series, managed at last to find a perfect length that forced his opponents to jump back or play forward fearing for their front teeth.
The left-handed Jacques Rudolph followed shortly after tea, completing his wretched series by leaving a Bicknell inswinger that clipped the top of his off stump.
Neil McKenzie was last to go, television replays suggesting he had got an inside edge to Flintoff's delivery.
Harmison would probably had apologised but the all rounder punched the air in delight.
While South Africa will hope for rain on Monday, England will look to their bowlers to finish off what they have begun.
They will be aware of the size of that challenge. South Africa's last three wickets added 333 runs in two innings at Headingley.
South Africa second innings
G.Smith lbw b Bicknell 19
H.Gibbs c Stewart b Anderson 9
G.Kirsten c Trescothick b Harmison 29
J.Kallis lbw b Harmison 35
N.McKenzie lbw b Flintoff 38
J.Rudolph b Bicknell 8
M.Boucher not out 22
S.Pollock not out 19
Extras (b-1 lb-5) 6
Total (for six wickets, 57 overs) 185
Fall of wickets: 1-24 2-34 3-92 4-93 5-118 6-150
To bat: A.Hall, P.Adams, M.Ntini
Bowling:
Bicknell 18-43-51-2,
Anderson 10-1-55-1,
Harmison 13-5-24-2,
Giles 10-2-36-0,
Flintoff 6-2-13-1
