Show them the way, Harry. Leading from the front is the oldest playbook in the game for a captain whose words have been falling on deaf ears. All tournament, Brook has been urging his batsmen on, to no avail, and so it was time to show them how to do it himself: promoted to No3, Brook danced and dazzled to play one of the great T20 innings and secure a semi-final berth for his team.

Brook made his highest score in T20 internationals and became only the third England batsman to score hundreds across all three formats in the process, joining Jos Buttler and Dawid Malan in that elite club. He looked in a different class from anyone else in the match, striking the ball with rare power and authority, and he navigated the unorthodox challenge of Usman Tariq with skill and intelligence, opting to take fewer risks against him, while taking the attack to the others.

It means that England will have the luxury of playing their last match against New Zealand in Colombo on Friday under no pressure. They have qualified for the semi-finals in the past five T20 World Cups and will be hoping that, with Brook bang in form and, at last, batting in a position from which he can affect the game significantly, they can go one better than two years ago, when they were beaten by the eventual winners India at the semi-final stage.

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Brook revealed that the decision to move to No3 was prompted by the coach, Brendon McCullum, on the morning of the game. Brook should have batted higher earlier in the tournament, of course, but at least that oversight has now been corrected. With Buttler, who recorded another low score, so out of sorts, Brook is England’s best player by far and therefore needs to be given maximum opportunity, rather than coming in at No5.

There was also the identity of the opponents to consider. Pakistan will be sick of the sight of Brook by the end of his career if he continues against them in this way. He has a superb record against them in Tests, of course, having hit three hundreds on his first Test tour there and a triple hundred on his last, and before this match in T20 internationals, he was averaging 60 against them at a strike rate of 150. The sight of them seems to bring the best out of him.

It was not a one-man show, as England’s bowlers did their bit, particularly the less-heralded Liam Dawson, who took three for 24 in his four overs. But with the opening partnership spluttering again — Phil Salt was out first ball, and Buttler third ball — and the fielding shoddy at times, it was not a pitch-perfect performance. As against Sri Lanka, England could point to a very strong recent record against Pakistan and were good enough on the night again to stretch their unbeaten run to six matches against these opponents.

Pakistan have had problems with their batting throughout the competition, Sahibzada Farhan apart. He is the tournament’s leading run-scorer, ahead of Shimron Hetmyer of West Indies, but has enjoyed too little support. Once again, this powerful right-hander dominated the innings, making another merry half-century, but the periods when England’s bowlers looked truly under pressure felt few and far between.

For Pakistan’s supporters, the debate will once again settle on the role of Babar Azam, their all-format champion, whose place has been questioned constantly as the deckchairs have been rearranged to find the right fit for him. In his innings here, a sedate 25 off 24 balls, he gave the impression of a classical pianist in a rave, somewhat out of place. Pakistan’s innings felt under par.

Usman Tariq of Pakistan dropping a catch from the bat of Jacob Bethell of England during a T20 World Cup match.

Tariq fumbled a straightforward catch with Bethell on six runs…

SAMEERA PEIRIS/GETTY

Pakistan cricket players celebrate after taking a wicket against England.

… but the unorthodox spinner made amends when he removed Banton with his first ball

DIBYANGSHU SARKAR/AFP/GETTY

England’s fielding was shoddy at times, and they gifted Pakistan at least 15 runs. Jacob Bethell, normally so sure, gave away two misfields in the deep that went to the boundary; there was a no-ball and free hit following a sloppy moment when only three men were inside the inner circle (the extra ball in the over went for four) and Brook dropped a scorcher at extra cover that also went for four. There were numerous other fumbles.

England's captain Harry Brook playing a shot during the T20 World Cup cricket match against Pakistan.

Brook kept the pressure on the Pakistan attack as wickets tumbled around him

ERANGA JAYAWARDENA/AP

Those unforced errors began to look important when Shaheen Shah Afridi knocked back Salt and Buttler, both caught behind, and Bethell, caught in the deep, in the opening powerplay. Batting at No3 in a T20 international for the first time, Brook looked immediately at ease, taking Mohammad Nawaz’s first over, the sixth of the innings, for 16 runs, his footwork so crisp and sharp and his placement of the ball equally so.

With Tariq held back for the middle phase, it was clear that the battle between him and Brook was going to decide the match, the more so when Tom Banton edged the first ball he faced from Tariq to the wicketkeeper and when Sam Curran pulled a half-tracker to deep mid-wicket. Brook and Will Jacks opted for brain rather than brawn then, dialling down risk against Tariq and exploiting the decent-sized boundaries to run Pakistan ragged in the field. England scored 14 twos all told in their innings, a measure of this intelligent approach.

Jos Buttler walking off the field after being dismissed during the ICC Men's T20 World Cup.

Buttler’s substandard World Cup didn’t get any better, dismissed for two after his fellow opener Salt had gone first ball

SAMEERA PEIRIS/GETTY

Brook’s half-century had come in the tenth over, off just 28 balls, and his second 50 came in just 22 more. After a difficult winter, with criticism flying after England’s dreadful Ashes performances and his own poor off-field judgment in the New Zealand series that preceded it, Brook looked delighted when, in consecutive balls in Afridi’s final over, the 17th, he backed away and peppered the off side for a six and four, the second of which took him to his hundred. It was a special innings.

Liam Dawson of England celebrates the wicket of Mohammad Nawaz of Pakistan during the ICC Men's T20 World Cup.

Dawson stifled Pakistan in the middle overs, finishing with impressive figures of three for 24

MB MEDIA/GETTY

There was a wobble when Brook was then immediately yorked by Afridi. Jacks and Jamie Overton were dismissed in the penultimate over, but it felt like too little too late for Pakistan, and it was left to Jofra Archer to hit the winning runs, with five balls to spare. After their final super-eights contest with New Zealand in Colombo on Friday, England will head to India for their semi-final, opponents as yet unknown. Are they peaking at the right time? One thing is certain, Brook is now in the right position to make his presence felt. One more piece of the jigsaw has been put in place.

Baz the mastermind behind Brook promotion

Harry Brook hailed Brendon McCullum as the “mastermind” behind a late move up the order to No3 which fuelled his dazzling century off 50 balls, the fastest for England in any T20 or ODI World Cup competition, and the second fastest in a T20 World Cup by any player behind only Chris Gayle (Simon Wilde writes).

Brook said that England’s head coach came to him in the morning with the idea, saying, “What do you think about No3? Pakistan is your team.” Going into the game Brook averaged 70 against Pakistan across all formats. The rest of the team were told about the switch in a huddle on the outfield before the game started.

“Baz was the mastermind there,” Brook said. “He had the discussion with me this morning about going up the order, trying to maximise the powerplay and put them under pressure. Also, partly because of my past history against Pakistan. Thankfully, it paid off. I know we were losing wickets, but my job was still to try to go out there and put them under pressure throughout.”

Pakistan's Shaheen Shah Afridi shakes hands with England's Harry Brook during a T20 World Cup cricket match.

After bowling the Yorkshireman on 100, Afridi went straight over to congratulate Brook on a fine innings

ERANGA JAYAWARDENA/AP

Asked if he would stay at No3, Brook said: “I don’t know yet, that’s something for me and Baz to chat about. But the longer I bat, the better it is for me and it’s a lot easier facing their best bowlers through the middle period when you’re already set. It was a lot of fun. It’s always a lot of fun scoring runs. It’s a shame you just can’t do it every time.”

Brook had never previously batted in the top three in T20s for England, but it would be a major surprise if this proved a one-off, especially as the captain conceded that he had been thinking about moving higher up the order “for a while”. Brook also has a very good record against England’s next opponents, New Zealand, whom they play on Friday.

The Pakistan fast bowler Shaheen Shah Afridi, who has played alongside Brook in the Pakistan Super League, said he shook Brook’s hand after he got out because he had played “a world-class innings”, adding: “I have never seen a batsman like him. Today he was ready for every ball. He was really prepared for us.”