One last cross, one last chance for Rochdale to rescue the Wembley dream that had cruelly disappeared when Harry Kane scored an 88th-minute penalty for Tottenham. In it came, Spotland held its breath as it fell at the feet of Steve Davies and the substitute held his nerve to find the bottom corner. League One’s bottom club have their date under the arch after all. It was a fairytale ending, richly deserved and brilliantly executed.

Here was the FA Cup in all its majesty. One of the most financially stretched clubs in England stretched to the limit a team that outplayed Juventus in the Champions League five days earlier. Keith Hill’s side undeniably merited a second bite at their Premier League guests but a replay, one that will take their income from this season’s Cup run beyond £1m, seemed to have been ripped from them when Harrison McGahey tripped Dele Alli and Kane scored on the ground where he made his professional debut in 2011.

But Rochdale would not be denied. They had performed with spirit and no little quality throughout and, when Matthew Done’s cross broke for Davies off the head of Toby Alderweireld, only the most hard-hearted of Spurs supporters could have begrudged the precise finish that followed.

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Spotland erupted. Mauricio Pochettino patted the grizzly beard of his Rochdale counterpart Hill and exited down the tunnel. A relaid pitch proved to be the least of the Spurs manager’s concerns at Spotland where he made several changes, summoned both Alli and Kane from the bench, and ended up with an unwanted addition to his already demanding schedule. The replay will support Rochdale’s finances for the next two to three years, said Hill. Performances of this calibre will also assist their fight to avoid relegation to League Two. Hill’s side were exemplary and Pochettino had the good grace to say he was thankful to “still be alive” in the FA Cup.

The tone of an uncomfortable evening in Lancashire for Spurs was set when Alderweireld slipped on the relaid pitch from kick-off. Rochdale were entirely responsible for the troubles of the Premier League visitors, however, not a pitch that had drained £500,000 from a club that can ill-afford such a hit on its resources. Or could not before this Cup run.

Lucas Moura made his first start for Tottenham since his £23m move from Paris Saint-Germain and impressed with his penetrating runs and the cool finish that cancelled out Ian Henderson’s excellent opener. The link-up play between Fernando Llorente and Son Heung-min also tested the Rochdale defence but they were alert to Spurs’ quick intentions and gave their midfield the confidence to play with composure. Gradually, remarkably, Rochdale emerged as the more threatening team in a first half that made a mockery of their lowly league position and the gulf between the two clubs.

Rochdale’s midfield trio of Andrew Cannon, Callum Camps and Mark Kitching were outstanding. Henderson was a 33-year-old dynamo of relentless energy and dangerous movement in attack. The central defence of McGahey, Jimmy McNulty and Ryan Delaney were concentrated and powerful, although a bit too much when McGahey clattered into Harry Winks from behind and somehow escaped a card. They could not contain Spurs entirely – really, how could they? – but the visitors only seriously tested the Rochdale goalkeeper, Josh Lillis, once before the break. Lillis proved equal to Son’s low effort after the striker was put through by Llorente, who side-footed horribly wide when the South Korean returned the favour from the rebound.

The tie was played out amid a wonderful atmosphere that would have intensified earlier had Henderson converted two decent chances before his sixth goal in this season’s FA Cup arrived on the stroke of half-time. His first was placed too close to Spurs’ keeper and captain for the day Michel Vorm after Cannon had wrestled possession from Victor Wanyama in central midfield. His second was sliced across goal when picked out unmarked on the left of the Spurs’ penalty area. His third sight of goal produced a moment that will linger long in Rochdale’s history.

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Henderson’s breakthrough encapsulated their first-half performance. It stemmed from a challenge by Camps to deny Moura inside the Rochdale area. In an instant Hill’s team were on the counterattack and Cannon fired the perfect pass behind the visiting defence for the former Norwich City forward, who almost quit the game to study dentistry five years ago, to sidefoot a superb first-time finish into the bottom corner. Spotland shook in celebration.

The Champions League guests were facing an examination of their character as well as their application and, in fairness, they dominated the second half. Moura equalised in style on the hour when Llorente picked out his run into the area and he lifted an exquisite finish over the advancing Lillis for his first Tottenham goal. Wanyama missed a glorious opportunity when he volleyed over from two yards out but his embarrassment appeared to have been spared when Alli made the most of contact with McGahey, although there was contact, and Kane put away the resulting penalty. Rochdale were deflated but then came one final cross.