The visitors took a half-time lead after Mathieu Flamini tucked home in the 26th minute, but we hit back through a Calum Chambers own goal 12 minutes into the second period and were unfortunate not to take the lead during a spell of great pressure.
But the Gunners secured a place in the fourth round when Flamini thumped in a 20-yard volley in the 78th minute and we were unable to peg them back again despite a late flurry of chances.
Both teams fielded much-changed sides from the weekend’s Premier League games, with Federico Fazio making his first appearance of the season for us, while Aaron Ramsey was the only player who remained from the Arsenal side that lost to Chelsea.
As you’d expect from a North London derby, the atmosphere was buzzing inside the stadium as the game kicked off, but while there was plenty of commitment and endeavour from both sides, there was little to shout about in the early stages.
In fact it was 13 minutes into the contest before a sight of goal for either team and it fell to the visitors. Ramsey threaded a pass inside Kieran Trippier to Kieran Gibbs, his cross was cleared as far as Joel Campbell who nodded goalwards but over the bar.
Possession was fairly even but the goalkeepers weren’t being troubled, that was until the 26th minute when Arsenal grabbed the lead with the first shot on target of the match. Olivier Giroud played a ball in to Alex Oxlade-Chamberlain who rode a challenge 25 yards out and had time to line up a shot. His effort was saved low down by Michel Vorm but Flamini was quickest to the rebound and fired high into the roof of the net.
Stung by the setback, we started to carve out a few half chances, with Danny Rose at the heart of some good work down the left. Just after the half-hour mark a swift counter-attack led by Harry Kane saw Rose bursting from the back down the flank. He cut inside Debuchy but drilled wide with his right foot. Moments later, Rose controlled a cross-field ball on his chest to beat the defender and, as the ball ran into the area, he just beat David Ospina to it but lifted his effort over the bar on the stretch.
The visitors went close on 39 minutes when Fazio gave the ball away on halfway, Oxlade-Chamberlain broke clear but his attempted shot from the edge of the area didn't have enough curl and was always drifting wide of the far post.
In the closing minutes of the half, Andros Townsend clipped a cross to the far post which Kane controlled and laid off to Eriksen, his shot was blocked and the rebound almost fell to Tom Carroll but Arsenal cleared their lines.
And when a Gunners attack broke down on the edge of our area, Eriksen led the charge forwards, he passed out to Kane who surged into the area and fired goalwards from an angle but his shot went across the face of goal and behind as the half drew to a close.
We made a much brighter start to the second period and had the ball in the back of the net after three minutes, Kane sliding home from close range after Eriksen’s 18-yard shot had hit the post, but the flag was quickly up for off-side and it was ruled out.
Rose then made another surging run forwards only for his cross to be cleared by Per Mertesacker for a corner. Eriksen rolled the set-piece to the edge of the area where Townsend looked to find the far corner but Ospina saved comfortably.
It was certainly one-way traffic at this stage and the equaliser duly arrived. Trippier clipped a deep cross which came to Nacer Chadli, he got to the byline and delivered a low cross which was heading straight into Ospina’s hands until Chambers stuck out a leg to divert the ball into the back of the net and lift the decibel levels up inside the stadium!
The pressure continued to mount and when Townsend sent over a corner to the back post, Kane produced a superb scissor kick which was heading towards the back of the net until Gibbs cleared off the line.
Both teams added extra firepower to their ranks in the 67th minute, Heung-Min Son replacing Townsend for us while the visitors introduced Alexis Sanchez for Campbell. And, after Ramsey had dragged a shot wide after breaking from midfield, Sanchez was quickly in the action but fired tamely at Vorm.
Arsenal were enjoying a good spell themselves at this stage and when Ramsey threaded a pass in behind our defence, Vorm was out quickly to deny Giroud with a flick of his leg. Then came their second on 78 minutes. Fazio stuck a foot out to prevent Sanchez’s through ball from reaching its destination, the ball looped up into the air on the edge of the area and fell perfectly for Flamini to run onto and volley past Vorm.
With Dele Alli having already come on for Chadli, we made a final change five minutes from time when Clinton Njie replaced Dier and he almost made an immediate impact, glancing Eriksen’s cross just wide within seconds of coming on as we searched for an equaliser.
Neat build-up play between Carroll and Kane led to the latter laying a pass into the path of Alli on the edge of the area, but his shot was easy for Ospina. And, as we pushed in the dying seconds to force extra time, Arsenal broke away through substitute Theo Walcott although he dragged his shot wide and that was the final action as the whistle blew moments later.
Spurs (4-2-3-1): Vorm, Trippier, Fazio, Wimmer, Rose, Dier (Njie 85), Carroll, Townsend (Son 67), Eriksen, Chadli (Alli 75), Kane. Substitutes (not used): Lloris, Walker, Vertonghen, Winks.
Arsenal (4-2-3-1): Ospina, Debuchy, Mertesacker, Chambers, Gibbs, Arteta, Flamini, Campbell (Sanchez 67), Ramsey, Oxlade-Chamberlain (Walcott 89), Giroud. Substitutes (not used): Macey, Monreal, Bellerin, Ozil, Iwobi.
Goals: Spurs – Chambers (own goal) 57; Arsenal – Flamini 26, 78.
Yellow cards: Spurs – Alli; Arsenal – Arteta, Flamini, Debuchy.
Referee: Andre Marriner.