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.
“This series I have felt more consistent with bat and ball, especially ball. I felt good rhythm after the first game. I contributed with the bat a couple of times,” Ali told BBC Radio’s Test Match Special.
“In general, I’m very pleased,” the 30-year-old Worcestershire all-rounder added.
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.
“I’m very pleased, a fantastic effort,” said an elated Root.
“We knew the target was a lot of runs and we set off brilliantly with the new ball.”
South Africa, 43 for three at lunch, saw Hashim Amla (83) and captain Faf du Plessis (61) put on 123 for the fourth wicket after James Anderson, bowling from the newly-named James Anderson End on his Lancashire home ground, and Stuart Broad had made early inroads.
– ‘Relentless’ –
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.
“Broad and Anderson are relentless and our batting line-up wasn’t strong enough for them,” said du Plessis after a match that seemed set to mark the end of Russell Domingo’s tenure as South Africa coach.
“To lose Hashim and then the cluster of wickets was disappointing.”
Earlier, Ali, both the man-of-the-match and the hosts 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 — a match Ali ended with a hat-trick — fell for five on Monday when caught behind off Broad.
Heino Kuhn, struggling to cement his Test place, repeatedly played and missed before, on 11, edging Anderson to Cook.
Temba Bavuma again battled hard until, from off the last ball before lunch, he caught behind on review.
Amla completed a 100-ball fifty and then twice forced Stokes off the back foot for two stylish fours, before lofting Ali for six.
But with South Africa 163 for three, Amla missed an intended whip shot off Ali and was lbw, although England, had to review umpire Kumar Dharmasena’s original not out verdict.
No replays were required when Quinton de Kock (one) edged a drive off Ali to 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.