Set a formidable 371 to win, England chased down the target comfortably, ending on 373/5 in 82 overs to go 1-0 up in the five-match series.
Resuming Day 5 on 21 without loss, openers Duckett and Zak Crawley (65) put on a commanding 188-run stand, laying the perfect foundation. Duckett’s knock, full of authority and invention, kept England ahead even as India fought back with four wickets in the second session.
Jasprit Bumrah bowled a probing opening spell, while Shardul Thakur briefly lifted India’s hopes with the wickets of Duckett and Harry Brook in successive balls.
But Joe Root (53*) and debutant Jamie Smith (44*) combined for an unbroken 71-run stand to see England home with ease.
Smith sealed the win with a towering six off Ravindra Jadeja.
India will rue dropped chances and inconsistent bowling on a placid surface.
The second Test begins at Edgbaston, Birmingham, from July 2–6, with India needing a strong response to avoid falling further behind in the series.