Off-spinner Ali ended the south London ground's landmark match when, after having Dean Elgar (136) and Kagiso Rabada caught at first slip by Ben Stokes with the last two balls of his 16th over, he had Morne Morkel lbw with the first ball of his next -- although England had to first review umpire Joel Wilson's not out decision.
It meant Ali had become the 13th England bowler to take a Test hat-trick.
South Africa, set a mammoth 492 for victory, were all out for 252 after lunch, with Worcestershire all-rounder Ali taking four for 45.
But the way this series has see-sawed -- England won the first Test at Lord's by 211 runs and South Africa took the second at Trent Bridge by 340 runs -- will give the Proteas hope of bouncing back in Manchester.
South Africa resumed on 117 for four, with left-handed opener Elgar (72 not out) and Temba Bavuma (16 not out) having already helped the Proteas recover from 52 for four on Sunday.
Their more realistic, if difficult, goal was to bat out the minimum 98 overs on Monday's last day to salvage a draw.
Man-of-the-match Stokes, who'd taken two wickets in two balls on Sunday to dismiss Quinton de Kock and South Africa captain Faf du Plessis after making 112 in England's first innings 353, opened the bowling on Monday.
But it was not long before the gritty Elgar pulled and cut the seam-bowling all-rounder for two fours.
- Roland-Jones double -
=======================
But Middlesex seamer Toby Roland-Jones, who had followed up his stunning Test debut bowling innings return of five for 57 by dismissing star batsman Hashim Amla cheaply for the second time in the match on Sunday, eventually ended a stand worth 108 runs.
His full-length delivery struck Bavuma on the pad as the diminutive batsman got only half-forward.
Aleem Dar ruled not out but England reviewed the experienced Pakistani umpire's decision.
Replays confirmed the ball had hit pad first and indicated it would have hit middle stump.
There was no need for a review next ball as South Africa's 160 for five became 160 for six.
Vernon Philander, who'd spent much of this match off the field with a stomach complaint, inexplicably padded up to a Roland-Jones delivery that nipped back and was plumb lbw for a golden duck.
South Africa had something to cheer when the 30-year-old Elgar, batting with a bruised finger, scored his eighth century in 38 Tests by lofting Ali over mid-off for a 16th four in 149 balls.
Elgar was in sight of his Test-best score of 140 against New Zealand at Dunedin in March, when, after more than five- and-half hours at the crease, he prodded forward to Ali and Stokes did the rest.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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