Match Tied (St Kitts and Nevis Patriots win the one-over eliminator)
Victory, achieved with more than a day to spare, also saw Joe Root triumphant in his first Test series as England captain.
South Africa, set a huge 380 for victory, were bowled out for 202 shortly after tea on the fourth day when Ali took two wickets in two balls to remove Morne Morkel and Duanne Olivier.
That gave the off-spinner a return of five for 69 in 19.5 overs and 25 wickets in total in a series where he also scored 252 runs.
Moeen Ali finished the series with 25 wickets and 252 runs © AFP
This result meant England had won their first home Test series against South Africa since 1998.
It was also just South Africa's second defeat in 20 away Test series, their other overseas campaign reverse in that sequence coming against India in 2015/16.
South Africa, 43 for three at lunch, saw Hashim Amla (83) and captain Faf du Plessis (61) put on 123 for the fourth wicket.
But Ali then took three wickets for five runs in 11 balls – including the prize scalp of Amla – as the Proteas collapsed from 163 for three to 173 for six.
Earlier, Ali, both the man-of-the-match and the man of the series, made 75 not out off just 66 balls in England's second innings 243, having been dropped on 15.
That left South Africa facing a mammoth chase, with no side having made more to win in the fourth innings of a Test at Old Trafford than England's 294 for four against New Zealand in 2008.
South Africa's already difficult task was not helped when they lost both openers, leaving them at 18 for two.
Dean Elgar, who made a gritty second-innings hundred in England's 239-run victory in the third Test at The Oval, fell for five on Monday when caught behind off Stuart Broad.
Heino Kuhn, struggling to cement his Test place, repeatedly played and missed before, on 11, edging James Anderson, again bowling from the newly-named James Anderson End, to Cook.
Temba Bavuma again battled hard until, from the last ball before lunch, he was given out caught behind on review off Toby Roland-Jones.
Amla completed a 100-ball fifty with his ninth four, a pull off Ben Stokes.
He then twice forced Stokes off the back foot for two stylish offside fours before driving Ali for six.
But with South Africa 163 for three, Amla missed an intended whip shot off Ali and was lbw, although England, for the second time on Monday, had to first review umpire Kumar Dharmasena's original not out decision.
No replays were required when Quinton de Kock (one) edged a drive off Ali to Alastair Cook in the slips.
And 173 for five became 173 for six when Theunis de Bruyn fell for a duck, nicking Ali to slip fielder Stokes.
The end came quickly for South Africa, 182 for six at tea.
Du Plessis, who played at Old Trafford for Lancashire, had added just one to his tea score when he was caught behind off Anderson, England's all-time leading Test wicket-taker.
Anderson, who finished with three for 16, then had Kagiso Rabada caught in the covers.
Ali, appropriately, finished the match with Morkel holing out for a duck before Olivier, also out for nought, was taken by Stokes at slip.