Newport County’s club shop stocks a book chronicling their dramatic final-day reprieve from relegation last season, titled “The Great Escape”. Here they came within eight minutes of accepting pitches relating to another astonishing chapter of their history and a woefully off-colour Tottenham Hotspur, muddied and bruised, will feel mightily relieved not to be the subject.

This would have been an FA Cup upset for the pantheon; one to be weaved into the narrative set by teams like Sutton United, Wrexham and Shrewsbury Town. Perversely it was Harry Kane’s straightforward far-post finish, eight minutes from full-time, that gave truth to the home support’s vocal anticipation of a trip to Wembley but the League Two club would have merited even greater reward. Mike Flynn’s side played the occasion amid a raw, visceral, intensely involved atmosphere at Rodney Parade but they stood toe to toe with their opponents too; they scored a deserved opener through Pádraig Amond and, although Spurs’ pressure mounted in the final half-hour, they were hardly hanging on by the skin of their teeth when Kane finally did what he always does.

“I hear a lot that this competition is magic, and it’s magic because here, with a Premier League team and a League Two team, to be honest I didn’t see too much difference,” Mauricio Pochettino said afterwards. It was a humble assessment but there was no other conclusion to draw, particularly on the evidence of a first half in which Tottenham were outbattled and, at times, outplayed.

Pochettino had selected a side designed to deal with Newport’s physical strengths but his decision proved to be a leveller. He refused to blame a threadbare pitch, scarred by years of dual deployment between rugby and football, for his team’s lack of coherence, and the absence of excuses was refreshing. The way in which Joss Labadie, Newport’s outstanding captain, dominated the midfield through brain and brawn during the opening period had nothing to do with the surface and nor, to take another example, did the shakiness of Juan Foyth against a relentless front line.

One of those Newport forwards, Frank Nouble, should have opened the scoring within four minutes but produced a finish more suited to the oval ball game after fine work on the right by Labadie. A little composure would have provoked pandemonium among a raucous home support that, from the start, created the kind of atmosphere that Pochettino admitted he missed. “It’s reality, it’s pure passion,” he said of the environment; it became delirium when, after a breathless first 38 minutes from Newport, Amond struck.

The goal came from one of a series of long throws by Ben Tozer, a couple of which had already caused some consternation. This time the ball was cleared but only as far as the right-winger Robbie Willmott. In one of those time-honoured FA Cup feelgood tales, Willmott was stacking shelves in Tesco while playing non-league football for Bishop’s Stortford. Now here he was, clipping in a perfect delivery for Amond to rise above a static Kieran Trippier and put Newport in sight of history.

They were forced deeper as the second half progressed but Tottenham remained off-key. Kane had clipped a post in the opening period and Son Heung-min, introduced at half-time to spice up what had been a stodgy starting XI, drew a smart save from the legs of Joe Day. There was the occasional reminder from Roger East, the referee, not to time-waste, but when, shortly before Kane’s equaliser, Victor Wanyama stubbed his toe in slicing speculatively wide, it was tempting to think Spurs had run out of ideas.

That is never a sensible thought as long as Kane is prowling and his equaliser came after Son, improvising to pirouette a flick across goal from Trippier’s near-post corner, came up with an example of the quick thinking they had lacked. “It was the only mistake we made all day and we got punished,” said Flynn, who pronounced himself “gutted” but in a tone far more proud than mournful. Flynn explained that, once Tottenham had scored, his conscience would not permit him to send on attacking substitutes and risk losing what he estimated to be a £700,000 windfall for the club. Kane spurned a half chance to scupper his best-laid plans but a Tottenham win would have been a travesty.

“It can save clubs, not just keep them ticking over,” Flynn said of the benefits Newport had accrued from their afternoon. During 50 games in charge he has dragged them back from the brink of the National League to the point of an indelible place in FA Cup lore; it was not quite to be, not yet anyway, but the wave of celebrations at full-time bore ample testament to their latest achievement.