On a manic night on which bowlers were lambs to the slaughter, Yorkshireman Root kept his cool with a stunning example of short-form batsmanship, hitting four sixes and six fours in a decisive 44-ball stay.
England survived a last-over wobble to claim a remarkable two-wicket victory with two balls remaining, Moeen Ali punching the winning single.
Only the West Indies, who made 236 against the same opponents last year, have ever scored more to win an international and England’s mark has never been bettered in domestic T20s.
At the halfway stage, having seen the Proteas rack up 229-4, England appeared to be on the way out of the World Twenty20, but they chased fearlessly from ball one - Jason Roy setting the tone with 43 in just 16 deliveries.
South Africa will look to their own indiscipline having shipped 20 wides, while England’s bowlers will breathe a sigh of relief having been pulled apart on an admittedly unhelpful pitch.
England had watched Quinton de Kock (52and), Hashim Amla (58) and JP Duminy (54no) pile on rapid-fire runs and came out inspired rather than intimidated.
Roy batted with frantic brilliance, hitting half of his 16 deliveries to or beyond the boundary.
Hales was dropped first ball off Dale Steyn but still managed four boundaries as the world’s No 1 bowler disappeared for 23.
The numbers were incredible: 44 off two overs, 65 from four, 89 from six, outgunning what had come before.
But England were losing wickets too. Roy ramped Kyle Abbott for six then lobbed a catch attempting a repeat, Hales was pinned lbw on the crease by the same bowler and Ben Stokes - promoted to No 3 - plonked a Kagiso Rabada full toss straight to Chris Morris in the deep.
It was a thrilling spectacle and delighted the crowd.
South Africa halted things with spin, Duminy and Imran Tahir sharing four overs for 29, with the latter also persuading Eoin Morgan to drag one into his stumps.
That brought together Root and Jos Buttler, and the pair added 75 in six overs that tilted the momentum.
Root swatted Duminy for six, guided Morris over third man then helped take 12 more off Steyn’s second over.
He saved the best for Morris, reverse flicking the all-rounder for six more with brilliant timing.
Buttler added 21 from 14 balls but was stumped off Tahir, despite De Kock’s late fumble.
England required 42 from the last five overs and Root took 10 off Abbott’s next two balls, a neat flick for four and a clean hit down the ground.
Morris could not keep Root quiet, leaking four more boundaries in the 18th, but the Yorkshireman fell just before the line.
It took a Rabada full toss, heaved into the deep, to get him but he had a long pep talk with Moeen as he left.
The scores were tied with one Abbott over to go but Chris Jordan and David Willey fell to consecutive balls, the latter nervily run out.
Moeen ended the drama by driving one past mid-off and punched the air to seal the end of a wonderful contest.
Earlier, after Willey’s first over cost just two, De Kock stroked a Reece Topley loosener for six over point and South Africa never looked back.
That over cost 15 and Willey’s next shipped 20 as De Kock battered two sixes and two fours from gentle offerings.
Moeen saw two of his first three balls hit the ropes but drew a mis-hit from Amla with his fourth.
Topley, licking his wounds at mid-off, flapped at the chance and grassed it.
It was a drop that cost 49 as Amla made hay, four of which came off Moeen’s very next delivery.
South Africa had 50 off just four overs but worse was in store as Jordan served up a selection of half-volleys and leg-side lollipops.
Relief finally came when De Kock dragged Moeen straight to Hales on the ropes, and continued when an ominous-looking AB de Villiers played for an Adil Rashid googly that never came.
South Africa reached 193 for four by the 18th over before Duminy and David Miller (28no off 12) smashed the chosen death bowlers - Topley and Jordan - for 18 apiece to close the innings.
Happily for England, there was more of the same to come.