England lost all five remaining wickets on the opening morning, with captain Alastair Cook (176) and Matt Prior (91) being the key dismissals for the home side.
Pragyan Ojha took 4-120 as England was dismissed for 406 all out, setting India just 77 to win.
India reached the target off just 15.3 overs, with Virender Sehwag the only man to fall for a quick-fire 25 off 21 balls.
Cheteshwar Pujara top-scored with 41 not out, while Virat Kohli was left undefeated on 14 not out.
Pujara was given the man of the match award as India took a 1-0 lead in the four-match series.
