Samir Nasri and Marouane Chamakh had put us in complete control as we looked set to leapfrog Chelsea, who play Birmingham later this afternoon.
However, Spurs - who had just one Premier League away victory over their old rivals, in May 1993 - regrouped for the second half following the introduction of fit-again England striker Jermain Defoe.
Gareth Bale pulled a goal back on 50 minutes, before a handball from Cesc from a free-kick gave away a penalty, which Rafael van der Vaart converted.
We were then condemned to successive home league defeats for the first time in 13 years when Younes Kaboul headed in a dramatic late winner.
There had been plenty of pre-match hype, and Arsenal midfielder Nasri kept his pre-match vow not to shake hands with William Gallas, his former team-mate for both club and country, handed the captain's armband this afternoon.
The pair then clashed within the opening few moments when Nasri raced clear, only to be halted by a fine saving tackle from the former Gunners defender, roundly jeered by the home fans.
It was a positive start for us, with Fabregas getting into the right side of the Spurs penalty area, but opted to shoot across goal rather than pull the ball back for Nasri.
Gomes flapped at a cross, before the Brazilian then hit the self-destruct button on nine minutes.
Fabregas' chip split the Tottenham defence, but Nasri's touch into the penalty area was just too heavy, which should have allowed Gomes to come off his line to collect.
However, the Spurs keeper hesitated and failed to gather the ball on the penalty spot, which then bobbled wide.
Nasri was alert to tuck his shot back from the tightest of angles between Benoit Assou-Ekotto and the far post.
Spurs were visibly stunned and for a while were in danger of being over-run.
Gallas, though, charged forwards right up to the edge of our box, but his progress was halted by Alex Song.
At the other end, Fabregas played his way into the right side of the Spurs penalty area, only to then drag a low shot wide.
We finally went 2-0 ahead on 27 minutes. A swift counter-attack saw Fabregas feed Andrey Arshavin on the left, and his low centre was turned in by Chamakh, his ninth of the season.
Harry Redknapp made a change at the start of the second half when he introduced Defoe for a first start since he played for England against Switzerland during early September.
It proved an inspired tactic as Spurs pulled a goal back five minutes after the restart.
Assou-Ekotto launched a long pass up field, which Defoe nodded down to van der Vaart and the Dutchman then tapped to the on-rushing Bale, who coolly slotted the ball into the bottom left corner.
From a position of such dominance, we were now the ones in danger of losing shape, as Modric fired just over from 20 yards.
As the hour mark passed, there was a break when Gallas bundled over Chamakh to concede a free-kick 30-yards out, which Nasri fired into the wall.
Song then barged Modric to give away a dangerous piece in a similar position for Spurs.
As van der Vaart struck the free-kick, Fabregas and Chamakh, on the end of the wall, both lifted their arms, leaving referee Phil Dowd with little option but to point to the spot.
Van der Vaart sent Fabianski the wrong way to equalise - sparking wild celebrations from the travelling support behind the goal and earning the Spurs man a caution.
Wenger immediately responded by sending on Robin van Persie, for Chamakh, on 68 minutes.
We had the ball in the net after a free-kick, but both Fabregas and Sebastien Squillaci were offside.
Spurs sent on Peter Crouch, replacing Roman Pavlyuchenko, before with 15 minutes left, Theo Walcott and Tomas Rosicky came on for Arshavin and Nasri.
Gomes redeemed himself with a fine one-handed save to deny Fabregas, with Laurent Koscielny heading over after the corner was not cleared.
Spurs, though, turned the game on its head with five minutes to go when Koscielny fouled Bale on the nearside touchline.
Van der Vaart floated the free-kick into the penalty area, where Kaboul got between his markers to guide the ball into the far corner.
There were five minutes of stoppage time, during which we pressed, but Spurs were not to be denied a famous win.