Harry Kane scored the only goal of the game - and his 32nd of the season - in front of a Premier League record attendance of 83,222 as Spurs claimed local bragging rights in addition to dealing a potentially fatal blow to Arsenal's hopes of finishing in the top four this season.
The Gunners could now end the weekend eight points adrift of the Champions League places, whereas Spurs move above Liverpool and Chelsea, who do not play until Sunday and Monday respectively.
The match got off to a quick start with Spurs applying the main early pressure, but the opening goal nearly came through an Arsenal boot when Shkodran Mustafi - who broke the deadlock at the right end in the reverse fixture - almost turned Dele Alli's low pass into his own net.
Petr Cech spared his teammate's blushes, and the Arsenal keeper - who passed a late fitness test to start - was called upon again after 18 minutes when he got down to make a comfortable save from Christian Eriksen's tame long-range strike.
Arsenal's first sight of goal arrived shortly afterwards when Hector Bellerin's cross was deflected into the path of Jack Wilshere, but the England international completely missed the ball with his right-footed effort.
Wilshere's air-shot was symptomatic of a first half which was short on chances and lacked any real quality in the final third, although Spurs did create the outstanding opportunity of the opening 45 minutes.
The chance fell to the man Spurs would have wanted it to as well, as London derby specialist Kane beat the offside trap to meet Eriksen's wicked delivery, only to put his header well over the crossbar when he should have done better.
Mousa Dembele then fluffed his lines when a loose ball fell to him on the edge of the box, and a tactical first half ended goalless with only one shot on target before the interval.
Spurs more than made up for the lack of usual intensity and energy associated with a North London derby by coming flying out of the blocks in the second half, though, with Kane finally breaking the deadlock just four minutes after the restart.
Cech had got away with a risky piece of goalkeeping moments before, but there was nothing he could do about the opener as Kane rose imperiously inside the area to meet Ben Davies's pinpoint delivery with a firm header which nestled into the bottom corner.
The goal sparked a period of dominance for Spurs during which Kane could have scored a hat-trick in the space of five minutes, with the league's leading marksman missing an easier chance than the one which led to his goal moments earlier when he glanced Eric Dier's cross inches wide of the target.
The rampant hosts were on the front foot once again within minutes, though, and this time Kane's ferocious volley from the edge of the area stung the palms of Cech, who was relieved to see it fired straight at him.
Eriksen was the next to come close when his free kick from just outside the area was tipped over by Cech, and Jan Vertonghen met the resulting corner but could not steer his header on target.
Spurs continued to dominate, but Arsenal finally called Hugo Lloris into action for the first time with just over 20 minutes remaining when the Tottenham keeper was at full stretch to deny Wilshere's wicked curling effort from the edge of the box.
It was a rare foray forward for the Gunners, though, and Tottenham were quickly back on the search for a second goal when Son Heung-min blasted a presentable chance well off target.
The growing pressure even appeared to be getting to the veteran Cech, who was let off the hook for another risky piece of goalkeeping moments later when his pass was cut off by Alli, who could not keep it under control to punish the mistake.
Alli had a better chance seconds later as Spurs ran riot over an Arsenal defence in disarray, but with Cech this time in no-man's land the Tottenham midfielder could only poke a tame effort wide of the target when he should have done better.
It wasn't long before Cech was keeping the visitors in the game, though, and he made a crucial save to deny Erik Lamela in the 72nd minute after the Argentine had been played through and left with only the keeper to beat.
Yet another chance arrived for the hosts four minutes later when a cross from the left fell at the feet of Kieran Trippier, but once again Cech came to the rescue for Arsenal by palming away the full-back's first-time half-volley.
The Gunners keeper was being afforded minimal protection from those in front of him - a stark contrast to the first half - but Spurs were unable to make them pay, with Lamela dragging another effort wide from a tight angle after being left with all the time he wanted to pick a shot.
Every missed opportunity will have made the record crowd inside Wembley all the more nervous that they could be made to rue their profligacy, but when the time came Spurs were relieved to see that Arsenal were just as wasteful.
Alexandre Lacazette made a mess of one chance in the first minute of stoppage time, but he was presented with an even better opportunity to make himself an Arsenal hero two minutes later when Alex Iwobi's pass released him clean through on goal.
The Frenchman - who has had to play second fiddle to Pierre-Emerick Aubameyang since the latter's January arrival - got the better of Davinson Sanchez and was left with only Lloris to beat, but he slid his finish wide of the far post.
Even then Spurs were not out of the woods as Arsenal won a free kick on the edge of the box beyond the allotted stoppage time, but Mesut Ozil's effort went straight into the wall as Arsenal failed to steal what would have been a smash-and-grab draw against their North London rivals.
The win means that Spurs have now won five games in a row at Wembley for the first time and have kept five consecutive home clean sheets for the first time since May 2009, extending their unbeaten streak to 12 matches across all competitions in the process.
More importantly, though, Mauricio Pochettino's side move up to third in the Premier League table, with Liverpool taking on Southampton on Sunday and out-of-form Chelsea facing West Bromwich Albion on Monday night.
Arsenal's top-four hopes look bleak, meanwhile, as they drop six points behind the Champions League places following their third away league defeat in a row and their seventh of the season.
The Gunners are now winless in their last 16 Premier League away games to members of the top five and could end the day closer to the bottom of the table than leaders Manchester City.
TOTTENHAM (4-2-3-1): Lloris; Trippier, Sanchez, Vertonghen, Davies; Dier, Dembele, Eriksen, Alli (Wanyama, 85'), Son (Lamela, 70'); Kane
ARSENAL (4-3-3): Cech; Bellerin, Mustafi, Koscielny, Monreal; Wilshere, Elneny (Iwobi, 65'), Xhaka (Welbeck, 86'); Ozil, Aubameyang, Mkhitaryan (Lacazette, 65')