That ended any hopes of England salvaging an unlikely draw and India quickly wrapped up the match in the second session, impressive Test debutant Jayant Yadav (3-30) claiming back-to-back wickets as the hosts wrested the initiative in the five-match series.
In desperation for something special, Ashwin finally delivered a shooter right in middle and leg in his 13th over of the day, and there was no way that Hameed could keep it away as he was trapped right in front for an agonising end.
Despite the defeat in Vizag, England captain Alastair Cook gave a vote of confidence to the tourists, saying that his counterpart Virat Kohli proved to be the difference between the two sides. But the lead was 404 and England had to chase down it in two and half days at a rough pitch.
With this victory, Virat Kohli remains undefeated in 15 Tests as India's Test skipper. The other India bowlers backed Ashwin up really well in this match, and they need to continue doing that, but it is great to see the man from Tamil Nadu bowling so well.
Kohli once again top-scored in the second innings for India with 81 runs, setting a target of 404 for England.
Batting first, centuries from Kohli and Cheteshwara Pujara inspired India to 455 in the first innings. The question was if Kohli could do it in the slower batting conditions of Visakhapatnam. "But it also makes me not hit the ball in the air which I probably prefer in Test cricket". He had been so solid in defence in the first innings, and continued his tried-and-trusted methods in a 33-ball stay. It seems that he will have a longer run in the Test team.
Meyer, Harbaugh have a chance to recharge a rivalry
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Kohli also had special praise for Bengal pacer Mohammad Shami, who has returned after a knee surgery that kept him out mostly past year.
England was bowled out for 158 runs in the second innings.
India's premier spinner Ravichandran Ashwin was the pick of the bowlers, though, having finished with a match-haul of eight wickets.
Shami also dismissed Adil Rashid with a short-pitched delivery just before lunch and an Indian win was only a matter of time from there.
Stuart Broad bowled nearly 30 overs with a strained tendon in his right foot in the second Test against India - and is hoping his efforts may yet help salvage a stalemate. He was initially given not out but the third umpire overturned the decision to seal England's fate with Bairstow unbeaten on 34.