With one day to go England may have slept more soundly than their opponents. They led by 163 runs with 10 wickets in hand and with Alastair Cook unlikely to set a tantalising target so early in the series the least they can anticipate from this game is a highly respectable draw.

That would constitute a confidence-boosting start to the India section of the tour after the traumas of Dhaka. But in a sense this may be the least important consequence of such an encouraging day’s play for the England camp.

Trevor Bayliss in the dressing room, Andrew Strauss up in the VIP seats and Cook out in the middle have witnessed the advance of one or, possibly, two cricketers who might be of benefit to England’s Test team in the years to come.

Top of that list is the latest recruit, Haseeb Hameed, Cook’s latest partner and one to whom he might stay faithful for rather longer than he did with his predecessors. Hameed registered his first half-century in his second Test innings and finished the day unbeaten on 62. This is an important landmark, applauded by his family in the stands, but it was the manner of his innings that had eyebrows heading heavenwards.

Hameed had just been in the field for 162 overs, spending much of the time under the lid at short-leg, where he held three catches of varying degrees of difficulty. Out he came with Cook for a potentially tricky examination by the India spinners on a surface where the ball was starting to grip.

He acquitted himself with composure, playing late in the approved manner with hands as soft as marshmallows. Then he startled us. One stride down the pitch and he drove a delivery from Ravindra Jadeja back over the bowler’s head for six exquisite runs. It was the second six of Hameed’s career: the first was a hook shot against Middlesex’s Toby Roland-Jones.

There followed deft cover drives and late cuts against the spinners as well as flicks off the toes against the quick bowlers. All the while his bat was straight in defence.

This felt like a little innings that heralds the arrival of an opening batsman who will play more than the statutory seven afforded many of Cook’s recent partners.

We know more about Adil Rashid and in Test cricket this has often led to a focus upon his frailties. But this was one of his best days as a Test bowler. Four for 114 from 31 overs may not sound like a watershed performance – and perhaps it is not – but Rashid spun the ball sharply, more dangerously than his counterpart, Amit Mishra, has managed and his accuracy was better than in Bangladesh. One sensed him earning his captain’s trust as well as some respect from the India batsmen, who started the day on 319 for four.

Their progress to 488 did not come from the most obvious source, though Ravi Ashwin’s all-rounder status has been in the ascendancy for some time. He was last out for a typically well-judged 70, without which his side might have been seriously embarrassed.

The more obvious threat for England came from Virat Kohli and Ajinkya Rahane. They began as if they would be around for a long time. Cook opted for his pacemen, but there was no movement for them so he switched to spin and was soon rewarded. Rahane attempted an optimistic pull against Zafar Ansari – the ball was too full – and was bowled.

Three overs later, Kohli was out for the first time in his Test career hit wicket. Quite properly this counts to the bowler. Kohli pulled a ball from Rashid that was not that short and set off for a run, but he knew – and soon so did Jonny Bairstow – that his left boot had just clipped the stumps before he had completed his shot. A bail had dropped innocently to the ground and the India captain had to go.

Understandably, Rashid’s confidence soared after this. He spun his leg-breaks sharply and beat the outside edge several times, more often when the bat was in the hands of Wriddhiman Saha rather than Ashwin. Seeing Rashid bowl as well as he ever has for England Cook was loth to take him off. He may have kept him going for an over or two too many – there is much to be said for resting a bowler when he is still on top of his game rather than waiting until there is no option but to remove him from the attack.

For the bulk of the time Cook had his spinners bowling in partnership with pacemen. One end of the pitch is barer and there the ball gripped more readily. After lunch, Moeen Ali replaced Rashid and India were happy to dig in – it may be that Ashwin could recognise a deteriorating pitch and the obvious dangers of a substantial first-innings deficit. Moreover, Moeen and his partners were on target.

Just before drinks Moeen’s persistence was rewarded when Saha edged an attempted cut and now the game speeded up. Jadeja hit a majestic straight six off Rashid, but soon after a leg-break spat, took his glove and lobbed to Hameed at short leg.

Umesh Yadav was flummoxed by some high-quality leg-breaks from Rashid and sliced the ball on the off-side but it required Ben Stokes’s athleticism to take the catch. One run later – with India on 460 for nine – the innings should have been over. Cook, usually so reliable, dropped a straightforward slip catch to his obvious exasperation; the bowler, Stuart Broad, was none too pleased either.

That blemish cost England 28 runs as Ashwin farmed the strike cleverly, perhaps too cleverly for Mohammed Shami, who, given a rare opportunity, picked Rashid’s googly and then leathered it over the midwicket boundary. Eventually, Moeen had Ashwin caught in the deep for a much-deserved second wicket.

England’s spinners had bowled far more impressively than on the raging turners of Bangladesh. Meanwhile, their pacemen had bowled with unrelenting commitment and energy and with barely a flicker of the reverse swing that is so often their ally. They will not have to bowl for too long on the final day.