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A crate of beer awaited Lincoln City players when they returned to their dressing room after prolonged and hugely deserved celebrations at Turf Moor. “We got rid of it,” revealed the manager, Danny Cowley. “We are a professional team and we are mid-journey, although I noticed Alan Power had one in his hand.” It was no way to toast a slice of history, but an insight into why Lincoln are the first non-league team since 1914 to reach the quarter-finals of the FA Cup. The Imps are one win from Wembley.

The Cowley brothers, Danny and assistant Nicky, have revitalised Lincoln since leaving their jobs as PE teachers last year, guiding the club to the top of the National League and the last eight of the FA Trophy. They were confident and meticulously prepared for this fifth-round tie at Burnley, breaking the game into six 15-minute segments and arriving with confidence. “Our subs were celebrating with every 15 minutes that remained scoreless,” the manager said. But nothing really prepared them for this – one of the greatest shocks and achievements in FA Cup history.

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Sean Dyche made six changes from last weekend’s draw with Chelsea but this was not another example of a Premier League manager killing enthusiasm for the FA Cup with a makeshift team. Burnley were strong and recognisable. They were also contained, outplayed for a sustained spell in the second half and driven to distraction before Sean Raggett drove them out of the competition with his 89th-minute header.

Set pieces were a key part of the Cowleys’ buildup and that the winning goal stemmed from a corner – a poorly defended corner admittedly – underlined the professionalism they have brought to Sincil Bank along with their view of post-match drinking.

Only after Raggett, a £50,000 signing from Dover Athletic, opened the scoring did Lincoln come under sustained pressure with their goalkeeper Paul Farman saving twice at the feet of Andre Gray. They deservedly survived five minutes of stoppage time before celebrating with a delirious throng of 3,210 travelling supporters packed in the David Fishwick stand, behind the goal where history was made.

Most of the fans had been on the road by 8am for the early kick-off. They did not feel inconvenienced when the final whistle blew. Lincoln have made around £1m from this Cup run but money does not measure their impact on a competition that can appear in the death throes as a result of Premier League ambivalence.

Burnley were “dragged down to our style”, said Matthew Rhead, and the wardrobe-sized striker was not wrong or disrespectful to his own team. His running battle with Joey Barton ensured the Burnley midfielder suffered one of his disciplinary disappearing acts, throwing himself to the ground after running into Rhead’s arm and shoving his hand into the face of Terry Hawkridge, who evened up the theatrics when collapsing from a push by Jon Flanagan.

The needle worked. “He got upset when we were on top a bit in the second half. I love that,” said Rhead of Barton’s loss of control. “As soon as we dragged them into our style of football we knew we had a great chance of winning. He trod on my foot and then ran into my arm; it was completely accidental.”

Barton later tweeted: “Wasn’t trying to get the Big Man sent off. It was my job to front-screen and disrupt him. Was trying to get back in front of him.”

Rhead was a towering distraction to Burnley’s central defenders. Alex Woodyard and Power were ferocious in the challenge but composed on the ball in midfield. Lincoln’s central defenders, Raggett and the captain, Luke Waterfall, were disciplined and commanding – and would combine to devastating effect at the opposite end of the pitch.

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Dyche, no stranger to cup shocks as a Chesterfield player, said “all credit to them” throughout his post-match press conference but did not come across as gracious in defeat. “They have a back four that don’t go anywhere and play it to the big man,” the Burnley manager claimed. “They approached it as a lower league team should – with organisation rather than flair, by keeping it simple and not overthinking it.”

There was more to Lincoln’s display than Dyche gave them credit for. The visitors should have taken a well-worked lead from their first attack when Nathan Arnold twisted inside James Tarkowski and set up Jack Muldoon for a clear opening he side-footed over.

It was 27 minutes before Farman was tested in the Lincoln goal, from a tame effort by Gray, and though Sam Vokes, Barton and Scott Arfield all went close in the first half there was no time when Premier League authority threatened to take command of the tie. The longer it wore on, the more a Lincoln winner assumed an air of inevitability.

There was one minute of normal time remaining when Sam Habergham swung over a left-foot corner from the right and there was Waterfall, the powerful Lincoln central defender, left astonishingly unmarked at the back post. He headed across goal towards Raggett and his defensive partner steered the ball just over the line before Tom Heaton could claw it to safety. History in the making.