Set 310 from a minimum of 49 overs, England bowlers put the Indian batsmen under huge pressure by picking up wickets regularly.
Indian ended the play at 172 runs for the loss of six wickets.
Indian Test skipper Virat Kohli (49*) and Ravindra Jadeja (32*) ended the day as they added 40 runs in the seventh wicket partnership to save the match for the home side.
The hosts were put under pressure as they lost the wickets of R Ashwin (32) and Wriddhiman Saha (9) in quick intervals as Indian were left tottering at 132-6.
Jadeja and Kohli then spoiled England's ambition to start the series with a victory.
Adil Rashid took three wickets for England.
Alastair Cook (130) and Haseeb Hameed (82) shined with their willows as England declared at 260-3.
Amit Mishra picked up two wickets for India.
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