With India taking an unassailable 3-1 lead in the five-match series via a five-wicket win in Ranchi, it marked England's first series loss under the captain-coach duo of Stokes and Brendon McCullum.
Sarfaraz, who was fielding in the deep, was called by Rohit to change his position from long-on to silly mid-off, and while the youngster responded to his captain's call, he decided to take a big risk.
Kuldeep then dismissed Tom Hartley and Ollie Robinson in four balls, before Ashwin raced to his fifth wicket as stumper Dhruv Jurel took a brilliant reflex catch to oust James Anderson.
For the first 90 minutes, the pitch seemed ordinary, but then it revealed its bag of tricks, expertly exploited by Ashwin and Kuldeep to claim crucial wickets
India began day three with 134 runs behind, but Jurel and Kuldeep Yadav (28 off 131 balls) shared a crucial 76-run stand for the eighth wicket to help the hosts fight back in the match.
England's final three wickets fell for just six runs in 17 balls, with Ravindra Jadeja taking two of them, finishing as India's standout bowler with figures of 4-67.
Akash Deep, who claimed 11 wickets in four games for India 'A' against England Lions last month, inflicted most of the damage with his impressive 3-24 spell on a crack-ridden pitch.
Rohit Sharma (131) and Ravindra Jadeja (112) struck fine hundreds while debutant Sarfaraz Khan made a promising start to his Test career with an impressive 62 off 66 balls.