England were 102-3 with Joe Root batting on 35 at the Saurashtra Cricket Association ground before capitulating.
At lunch, England were 102-3 with Joe Root batting on 35 at the Saurashtra Cricket Association ground, hosting a Test for the first time.
Hameed, 19, who became the youngest player to open the batting for England on debut, made 31 during his 98-minute stay at the crease before falling lbw to world number one ranked spinner Ravichandran Ashwin.
Ashwin (2-35) also dismissed Ben Duckett for 13 after skipper Alastair Cook elected to bat on what seemed a placid wicket.
Hameed as well as Cook (21) benefitted from the largesse of India's fielders who were guilty of dropping several early chances.
Cook was dropped off Mohammed Shami off the third ball of the innings while Hameed got a reprieve on 13 when Murali Vijay grassed his catch at first slip.
The England skipper, who surpassed Michael Atherton's record of 54 Tests as England captain, was adjudged leg before off left-arm spinner Ravindra Jadeja (1-26).
TV replays showed the ball would have missed the leg stump but Cook did not refer to the third umpire even though the decision review system is being used for the first time by India in a home series.
Hameed showed little signs of nerves against top-ranked India, twice hitting Shami for boundaries in an over and driving Ashwin for an elegant four in the covers.
But he was trapped leg before by Ashwin, a decision which was upheld on review, just when the batsman appeared to be growing in confidence.
Earlier India opted to go into the match with five specialist bowlers, bringing in leg-spinner Amit Mishra to partner Ashwin and Jadeja.
England replaced Steven Finn with Stuart Broad who is playing his 100th Test after being rested from the side that lost the second match to Bangladesh in Dhaka.
The visitors also axed Gary Ballance to bring in Hameed and pushed Duckett down the batting order.