Spurs took control of the contest with two goals in the opening 40 minutes, both of which came as a result of Arsenal errors as first Christian Eriksen tapped home from close range and then Harry Kane converted from the penalty spot.
Alexandre Lacazette pulled a crucial goal back just before half time, though, setting up a blockbuster and breathless second half which contained chances galore and a prolonged siege on the Tottenham goal from the hosts.
Arsenal did find an equaliser through Pierre-Emerick Aubameyang, but both sides ultimately had to settle for a point despite their gung-ho attempts to claim all three in the closing stages.
Both managers made notable selection decisions as Mauricio Pochettino included Jan Vertonghen and Eriksen from the start for the first time this season, while Unai Emery started his £180m strike trio of Lacazette, Aubameyang and Nicolas Pepe together for the first time.
It took the latter less than a minute to have a sight of goal in his first taste of the derby, firing high and wide from the edge of the box after being found by Sead Kolasinac.
The Gunners maintained their quick start to keep Spurs pinned back from much of the opening 10 minutes, but the visitors struck against the run of play to draw first blood through the returning Eriksen.
Moments after Lacazette had dragged a long-range effort wide Tottenham launched a counter-attack, with Son Heung-min playing the ball through to Erik Lamela, whose tame right-footed effort forced a save from Bernd Leno. However, the Arsenal keeper could not hold on to the ball, spilling it at the feet of Eriksen to leave the Dane with the simplest of finishes for his 50th Premier League goal.
The strike saw Eriksen become the first Spurs player to register both 50 goals and 50 assists for the club in the Premier League era, while it was the 13th error leading to a goal committed by Arsenal since the start of last season - and the sixth by Leno - both of which are league highs.
It would not be the last or even the worst of the Arsenal defensive errors in the match, but the Gunners did survive further threats in the immediate aftermath of the goal as first Leno denied Eriksen before going some way to atoning for his mistake with a brilliant fingertip save from Son's curling effort.
Arsenal's pressure did begin to grow again as the half wore on, and it took an important block from Danny Rose to deny Pepe's header at the back post after being picked out by Aubameyang's cross.
Pepe then curled a free kick comfortably wide before Spurs began to threaten again at the other end, with Leno spilling a low strike from Kane and then pushing away a dangerous Eriksen free kick shortly afterwards.
An all-too-common moment of madness from Granit Xhaka gifted Spurs their second five minutes before the interval as the Swiss midfielder needlessly lunged into a rash challenge on Son inside the area, leaving referee Martin Atkinson with no choice but to point to the spot.
Kane stepped up and duly tucked a pinpoint penalty into the bottom corner - his record-equalling 10th goal in North London derbies and also the 19th spot kick to be scored in the fixture, which is more than any other fixture in Premier League history.
Arsenal immediately went on the front foot in an attempt to pull a goal back before half time, and they came close three minutes after Tottenham's second when Ainsley Maitland-Niles found Pepe, whose low strike was kept out by a smart Hugo Lloris save.
Lacazette then stung the palms of Lloris from a free kick, but fared better just seconds later when he collected Pepe's pass, beat Vertonghen and lashed a powerful effort past the Spurs keeper at the near post to halve the deficit.
The goal gave Arsenal some much-needed momentum heading into the second half, and the match quickly picked up its relentless pace upon the restart with Lacazette's header drawing another save from Lloris less than a minute after kickoff.
The Spurs shot-stopper got away with one moments later when his pass gifted possession to Aubameyang, and only a last-ditch challenge denied the Golden Boot winner a clear chance.
It was another open and end-to-end edition of the derby, and it almost swung firmly back in Tottenham's favour after 52 minutes when Son's low strike took a deflection off Xhaka and was then helped wide by the fingertips of Leno.
Arsenal were soon back on the front foot, though, and Lloris pulled off another fine low stop to deny Matteo Guendouzi's strike before Kolasinac somehow failed to convert Lacazette's flick-on from the resulting corner.
Lacazette then sent a dipping 30-yard volley wide of the target before Spurs came within inches of restoring their two-goal lead as the frenetic pace and non-stop action continued.
Lamela slipped a pass in to Kane, who in turn played a slick one-two with Eriksen before hammering a sweetly-struck shot against the inside of the post with Leno completely beaten.
Emery turned to Dani Ceballos off the bench in search of a creative spark to unlock the Spurs defence again, and the Real Madrid loanee almost made an immediate impact with a swerving long-range strike which Lloris needed to tip over the crossbar.
Ceballos's introduction did coincide with a period of dominance for the hosts, though, and they were well worth their equaliser when it arrived 19 minutes from time.
It was Guendouzi rather than Ceballos who came up with the defence-splitting pass, clipping a narrow cross into the box which Aubameyang poked beyond Lloris having timed his run to perfection off the shoulders of the Tottenham defenders.
Xhaka then tested Lloris with a long-range effort before Pepe blasted another opportunity wide having been left unmarked on the edge of the box from a corner, and Arsenal thought they had completed a remarkable turnaround 11 minutes from time when Rose bundled the ball into his own net from close range at the back post.
However, the offside flag was raised against Kolasinac in the buildup, and VAR confirmed the official's decision as Arsenal's ecstasy proved short-lived.
Just 1% of the play was in Arsenal's defensive third between the 70th and 80th minutes as they sent wave after wave of attacks forward and, while Spurs did begin to respond in the closing stages, the better chances continued to fall to the hosts and Pepe dragged another effort wide of the near post after a poor defensive header from Davinson Sanchez.
Spurs did have one penalty shout in stoppage time before Moussa Sissoko failed to make the most of a late opening, but the visitors will have been relatively relieved to escape with a point in the end despite having been two goals up at one stage.
Arsenal, meanwhile, will have mixed feelings after recovering from two goals down but also registering 26 shots on goal - just two fewer than they managed in their opening three league games combined.
ARSENAL (4-3-3): Leno; Maitland-Niles, Sokratis, Luiz, Kolasinac; Torreira (Ceballos 63'), Xhaka; Pepe, Lacazette (Mkhitaryan 67'), Aubameyang
TOTTENHAM (4-4-2): Lloris; Sanchez, Alderweireld, Vertonghen, Rose; Sissoko, Winks, Lamela, Eriksen; Son (Lo Celso 79'), Kane