Duckett followed the likes of Ian Botham in 1981 and Stokes himself in 2019 into Headingley folklore with a titanic fourth-innings knock to underpin a five-wicket win and a 1-0 lead in the five-match series.
England's last visit also produced another nail-biting finale, with Chris Woakes and Mark Wood bringing the 2023 Ashes alive by getting Stokes' side home in pursuit of 251 with three wickets to spare.
"We've been pretty good at this ground for the last few years," Stokes said. "We've got some good memories here and it's one more to add."
This was England's second highest successful pursuit ever, just seven runs off the target they reeled in against the same opponents at Edgbaston in 2022 at the outset of the Stokes-Brendon McCullum era.
"I think we're just a very simple-minded pair, me and Baz, when it comes to cricket," Stokes said.
"Everyone knows what cricket is about, it's about scoring more runs than the opposition. When you strip it all back, that's it. We try to keep everything simple and calm as we possible can.
"When you're chasing totals like that, how you are in the dressing room is very important."
Only Mark Butcher, with 173 at Headingley in 2001, has scored more among Englishmen in a fourth-innings win than Duckett, who was dropped on 97 but majestic in setting the tone for England on the final day.
A stand of 188 with Zak Crawley, who made a composed 65, provided ideal foundations as the openers took the sting out of India's formidable bowling attack to move past 2,000 runs as a partnership.
"Ducky has been incredible since coming into the team," Stokes said. "He's shown he can score runs pretty much all over the world in any conditions he's faced with.
"He's a quality player, such a hard person to bowl to with the new ball. I love the way that his natural game is to look to score and put bowlers under pressure from ball one.
"Ducky got the 149 but Zak was so, so important, too. They compliment each other so well. I'm sure you could ask the opposition bowlers about why they're a nightmare when they are in for a long period."
Jasprit Bumrah was wicketless and while India rallied to leave England 4-253 Â when Duckett and Harry Brook were out off successive balls, Joe Root's 53 not out and Jamie Smith's unbeaten 44 got them home with 14 overs still available.
While India will lick their wounds and look to regroup at Edgbaston for the second Test, starting next Wednesday, Stokes can feel vindicated after his decision to bowl first at the toss came under scrutiny.
India racked up 3-359 in glorious batting conditions after the first day and were at one stage 3-430 - they were also 4-333 in the second innings - but England fought back both times.
India coach Gautam Gambhir revealed they will not divert from their strategy to play Bumrah for only another two Tests, despite the rest of the bowling attack lacking a consistent cutting edge.
"We won't change the plans," Gambhir said. "To manage his workload is more important. Before he came on this tour, it was already decided he would play three Tests but let's see how his body turns out.
"We haven't decided which two other Test matches he's going to play. We absolutely have the bowling attack to take 20 wickets. We pick the squad on trust, not on hope."
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