The runs margin of success is in Englandās all-time top five, almost as emphatic as the 354 by which they beat the same opponents in Nottingham on their last tour six years ago.
It means too the scoreline is 1-1 with two to play, starting at Edgbaston next Wednesday.
But after James Anderson, Moeen Ali and Chris Woakes took three wickets each in Pakistanās 234 all out, the significant cloud on Englandās horizon is the extent of Stokesā calf injury ā set to become clear only after he undergoes MRI scans on Tuesday.
The all-rounder pulled up mid-over on the fourth afternoon, his first England appearance since he limped out of the action at Headingley in May and subsequently needed surgery on his left knee.
This time it was his right leg which gave way, leaving England to fire on four rather than five cylinders after Alastair Cook had left them 185 overs to bowl Pakistan out.
The captain, who courted controversy by failing to enforce the follow-on despite a mammoth lead of 391 the previous afternoon, hit an unbeaten 76 alongside Joe Root (71no) in a rollicking stand of 105 before declaring on 173 for one and setting Pakistan an entirely notional world-record 565 to win.
The relevant equation was not that, of course, but the task of taking 10 wickets inside five-and-a-half sessions.
It took less than five overs, in fact, before Anderson made the first incision when he yet again saw off opener Shan Masood cheaply.
Since the tall left-hander first faced Englandās all-time leading wicket-taker in Abu Dhabi last October, he has been out to him six times.
The latest was a tame edge pushing forward to one slanted across him.
It was Anderson who struck again too before lunch, number three Azhar Ali playing across a straight one to be lbw.
Pakistan would have been 32 for three, had Cook taken a regulation slip catch off Stokes when Younus Khan was on three.
It was a more significant setback for England when Stokes limped out of the attack, but they soon had two more wickets to celebrate ā both from Moeen.
The off-spinner, completing Stokesā unfinished over, was instantly struck over long-on for six by Mohammad Hafeez.
But he got his revenge when the opener fell bat-pad, eight short of his 50, and then Younusā attempt to hit Moeen for another six resulted instead in a running boundary catch for Alex Hales.
It was a bold option taken by the veteran middle-order batsman, with the man back on the fence, and one he paid for when he failed to clear.
A bigger blow still was to follow for Pakistan when their captain Misbah-ul-Haq, the only susbtance in their misfiring first innings, succumbed to a slower full-length ball from Woakes which he contrived to squeeze back on to his stumps from outside off.
Woakes doubled up immediately after tea, Sarfraz Ahmed caught down the leg-side off his glove.
England appeared to be on the last lap already ā and so it proved as Anderson pinned the only remaining frontline batsman Asad Shafiq lbw, and then man-of-the-match Root chipped in with a wicket-maiden in his solitary over as Pakistan subsided.
Cook had begun his vindication for spurning the follow-on when, in the first over of a cloudy and much fresher day, he took the opportunity against a weary attack to complete his fastest Test 50 when he cover-drove his 55th ball for four off Rahat Ali.
Root was in even more of a hurry, pulling Rahat for successive fours in an over which cost 14 as the Yorkshireman raced past 300 runs in the match.
After a favoured slog-sweep from a Yasir Shah full toss for his seventh four, Root had hit four of his seven boundaries in the space of six balls and was past his 50 in only 38 deliveries.
That was only six more than Ian Bothamās fastest English Test 50, and Root upped the ante to put himself on course to better Stokesā national record 85-ball hundred.
Nine overs had brought 75 runs, and a second century in the match would have taken Cookās record-breaking career tally to 30.
But for the collective good, he rightly called time before any more personal achievements became too tempting.