Match ends, Newport County 1, Tottenham Hotspur 1.
Mauricio Pochettino has said his Tottenham side, who were held by Newport County in the FA Cup, missed a "massive opportunity" to show they want to win a trophy this season.
Padraig Amond's header gave Newport the lead in the first half before Harry Kane's 82nd minute equaliser kept Spurs in the competition that they have won eight times.
Spurs have not lifted a major trophy since winning the League Cup in 2008.
"The team didn't really show they want to go next stage of the FA Cup. That is what has disappointed us," Pochettino said.
"The theory is to win trophies, and it's easy to talk about that. But I think we missed a massive opportunity to show we really want to win a trophy."
With Spurs having avoided a seismic Cup upset, Newport's heroic display will be rewarded with a lucrative replay at Wembley.
Kane captained a strong Spurs side, but they were rattled by a fervent performance from the League Two side and riotous atmosphere at Rodney Parade, which erupted when Amond headed the hosts in front.
After a dreadful first half, the visitors improved and dominated after the break and had several chances to equalise, with Kane heading over and Son Heung-min being denied by a fine save from Joe Day before Kane tapped in at the back post.
"We were very disappointing in the first half and it was only the last 30 minutes we started to play and create some chances," the Spurs manager added.
"I've heard in my years here that the FA Cup between a Premier League team and a League Two team is magic. But if I'm honest, I didn't see much difference."
Although victory against Premier League opponents who are 72 places above them in the football pyramid would have represented arguably the greatest result in Newport's history, a profitable replay at Wembley is an excellent consolation.
Having defied the odds to beat Championship side Leeds in the third round, the Exiles still have hopes of reaching the fifth round - with the chance of causing another shock - for the first time since 1949.
For Spurs, meanwhile, this was a major embarrassment narrowly avoided against a team who only preserved their Football League status with victory on the final day of last season.
"I'm gutted because we conceded so late in the game," Newport manager Mike Flynn said. "But they are a quality side and in the second half we couldn't really get at them.
"Wembley is something else for the club to look forward to. We were nearly there, we could taste it but we switched off [for] one minute."
Tottenham's culture shock
This was a culture shock for Tottenham, swapping the bowling green pitch and plush facilities of Wembley for the cramped changing rooms at Rodney Parade, the modest 140-year-old stadium their opponents share with two rugby teams.
Spurs were the first top flight team to play a competitive game in Newport since 1986, three years before the old Newport County went out of business.
This was the furthest the phoenix club - formed months later - have ever been in the competition and a record crowd for a football game of almost 10,000 crammed into the temporarily expanded ground to create a raucous atmosphere.
The hostility seemed to unsettle Spurs and, after three minutes, Eric Dier was dispossessed by Joss Labadie, whose low cross found an unmarked Frank Nouble, but his wild first-time effort flew high and wide.
That opportunity fuelled Newport's belief and they harassed their underperforming opponents, with captain Labadie the hosts' driving force in midfield.
One of his surging runs set the Exiles up for their opening goal. Spurs failed to clear a subsequent long throw and Robbie Willmott's deep cross was nodded in at the back post by Amond to spark deafening celebrations.
Even as Tottenham forced their way back into the tie in the second half, the Rodney Parade faithful continued to roar their encouragement, sensing their team were on the cusp of a historic result.
Kane's equaliser momentarily silenced the home fans but they were soon back at full volume and, at the final whistle, there was another eruption as Newport's supporters looked forward to the trip to Wembley, which their side's performance richly deserved.
Spurs avoid a shock
Tottenham's strong team selection was significant, demonstrating their respect for Newport and the FA Cup itself, perhaps their best hope of winning a first trophy for a decade.
Kane started for the second round in succession, having scored two goals as Spurs saw off Wimbledon in their previous outing in this competition.
The 24-year-old has struck 128 goals in 194 appearances for Spurs - but is yet to win a trophy.
Former striker Gary Lineker believes Tottenham face a "watershed moment" and, with the team fifth in the Premier League and facing Italian champions Juventus in the last 16 of the Champions League next month, the FA Cup could be their likeliest chance of silverware this season.
Lifting the trophy at their temporary Wembley home seemed a distant prospect during a first half at Rodney Parade in which Spurs were dreadfully sloppy.
With the exception of a Kane shot tipped on to the post by Joe Day, the visitors were way off the pace before the half-time introduction of Son brought some much-needed urgency to their performance.
And as Tottenham cranked up the pressure, there was a sense of inevitability to their equaliser.
Kane profited from Son's brilliant flick and, although this display was well below the standard Mauricio Pochettino has come to expect from his players, the manager's overriding emotion will be one of relief that his side could still make the FA Cup the first trophy of his tenure.
Man of the match - Joss Labadie (Newport County)
- 4LabadieBooked at 32minsSubstituted forDolanat 84'minutes
- 9AmondSubstituted forMcCoulskyat 74'minutes
- 21FoythBooked at 87mins
- 19DembéléSubstituted forDaviesat 81'minutes
- 37Walker-PetersSubstituted forSon Heung-Minat 45'minutes
- 18LlorenteSubstituted forAlliat 66'minutes
- 6D Sánchez
- 7Son Heung-Min
- Roger East
- Shots on Target
Second Half ends, Newport County 1, Tottenham Hotspur 1.
Corner, Tottenham Hotspur. Conceded by Dan Butler.
Corner, Tottenham Hotspur. Conceded by Ben White.
Attempt blocked. Harry Kane (Tottenham Hotspur) right footed shot from a difficult angle on the right is blocked. Assisted by Kieran Trippier.
Corner, Newport County. Conceded by Jan Vertonghen.
Offside, Newport County. Joe Day tries a through ball, but Shawn McCoulsky is caught offside.
Juan Foyth (Tottenham Hotspur) is shown the yellow card for a bad foul.
Foul by Juan Foyth (Tottenham Hotspur).
Matthew Dolan (Newport County) wins a free kick in the defensive half.
Corner, Tottenham Hotspur. Conceded by Ben Tozer.
Kieran Trippier (Tottenham Hotspur) wins a free kick on the right wing.
Foul by Shawn McCoulsky (Newport County).
Substitution, Newport County. Matthew Dolan replaces Joss Labadie.
Goal! Newport County 1, Tottenham Hotspur 1. Harry Kane (Tottenham Hotspur) right footed shot from very close range to the bottom right corner. Assisted by Son Heung-Min following a corner.
Corner, Tottenham Hotspur. Conceded by Ben White.
Attempt blocked. Eric Dier (Tottenham Hotspur) right footed shot from the left side of the box is blocked.
Substitution, Tottenham Hotspur. Ben Davies replaces Mousa Dembélé.
Attempt missed. Victor Wanyama (Tottenham Hotspur) right footed shot from outside the box misses to the right. Assisted by Dele Alli.
Mousa Dembélé (Tottenham Hotspur) wins a free kick in the defensive half.