England had never previously won two Tests in a single away tour in Pakistan, but Stokes and coach Brendon McCullum's side continued to make history as they wrapped up the victory on a hazy day in the City of Saints.
Mark Wood claimed two crucial wickets to swing the momentum firmly in favour of the tourists after Pakistan's 80-run seventh-wicket partnership threatened England's record.
However, the hosts were unable to sustain their pressure and, having started the day on 198 for four, requiring 157 more runs to win with six wickets remaining, they slid from 290-5 to all out for 328 chasing 355.
Stokes insisted England were aware of the magnitude of the occasion, as England secured their first series victory in the country since 2000-01.
"Coming into this game, being 1-0 up before we'd bowled a ball, I think we all understood what we could achieve before we started this game," the England captain said.
"We're not naive in the fact of what we know we've achieved here because we know how tough it is.
"Not just for English teams to come and win here but any team. Pakistan are a huge threat in their own conditions.
"Not for one minute are we going to think it's just another Test series win. Beating Pakistan in Pakistan is massive.
"We know what we've achieved, we know that it's a very special thing in English cricket to come here and win.
"It was a strange feeling there, the celebrations at the end winning the series just because compared to last week.
"We've got this bug still floating around the dressing room that we just can't seem to get rid of.
"I think it was just a sign of how tired the lads were there, mentally and physically. We know what we've achieved and another great win for us."
Saud Shakeel spearheaded Pakistan's resistance with the bat on the final morning, playing a watchful innings without taking risks for his 94 from 213, before he was caught by a diving Ollie Pope.
But England's seamers hit the right lines and length as Pakistan lost their final five wickets for just 38 runs, as the hosts suffered their second successive home series defeat having lost 1-0 to Australia in March.
Despite the historic win, Stokes urged his side to remain in the moment, and insisted that the reinvention of English Test cricket championed by himself and McCullum is bigger than individual match results.
"One thing we do is we stay in the moment. What did (Jack) Leach say - live where my shoes are, or something like that? Basically just always stay in the moment," the 31-year-old said.
"Don't take this kind of stuff and this kind of form for granted. And always just keep the mantra of, 'we're bigger than what we're actually doing at the moment'.
"What we're trying to do is bigger than results and all that kind of stuff, but obviously it massively helps when you are winning and in the way in which we are winning.
"The guys who I've got in the squad from the guys who step onto the field to the guys who unfortunately miss out on selection are all in it together. And we all really believe in what we're trying to do.
"It's a very special time to be an England cricketer."
Wood finished the match with six wickets and his dismissals of Shakeel and Mohammad Nawaz just before lunch turned the match back in England's favour when Pakistan looked like they might get over the line.
"I'm shattered," said the Durham quick. "It was hard-fought but that's when it's worth it in the end. Two games where the lads put so much in and, to get over the line, an amazing feeling really.
"I'm just absolutely knackered. To keep charging in and charging in was a big effort but we knew we were close and that's what really spurs you on.
"To see the other lads digging in, you don't want to let your mates down so you put in just as much.
"Stokesy said, 'make a difference, change the game', so that's what I tried to do. Those wickets were key. Nawaz, I thought the way he played was brilliant actually. That partnership was key to try and break."