India need 310 to win on fifth day of the first Test match in Rajkot after England declared their second inning for 260 for three.
Earlier, England captain Alastair Cook completed a well deserve century at the Saurashtra Cricket Association Stadium.
It was Cook's fifth century in India that put the visitors in a commanding position.
Earlier on day 4, after dismissing India for 488 and taking a slender 49-run lead in the first innings, the England openers started on a cautious note with the teenaged opener, Hameed getting to his maiden half century off 94 balls at the Saurashtra Cricket Association Stadium.
Coming in to bat in the post-tea session, the left-right opening combo frustrated the Indian bowlers as Cook and Hameed took England over the 100-run mark in the 33rd over.
Hameed, who consumed 116 balls for his undefeated 62, got a life, when the 19-year-old was batting on 40 after the third umpire turned down a leg-before review from the hosts.
Unfazed at the calls, the right-hander went on with his calculative stroke play hitting five fours and a six.
Cook, at the other end, maintained his composure and rotated the strike well as the southpaw took 107 deliveries for his knock, which contained just three hits to the fence.
For India, none of the bowlers looked threatening as even the spin trio of Ravichandran Ashwin, Ravindra Jadeja and Amit Mishra failed to extract the spin and bounce like their English counterparts.