Both Spurs goals came in a two-minute burst shortly before half-time with man-of-the-moment Gareth Bale and Aaron Lennon scoring before Arsenal hit back with a header from Per Mertesacker just after the interval.
But Arsenal failed to break down the Spurs defence again and they ended the day in fifth place on 47 points with their long unbroken run in the Champions League, dating back to 1998, under serious threat.
They have never finished below Spurs since Arsene Wenger became manager in 1996.
Although unsourced reports in Sunday papers said Arsenal were going to be the subject of a $1.5 billion takeover bid from Arab investors, failure to reach the Champions League would probably devalue that figure considerably.
Spurs, after years in Arsenal's shadow, seem to be the club on the move with victory bringing them to within two points of second-placed Manchester City who meet Aston Villa on Monday.
After missing out on Europe's elite competition last season, there is real belief at White Hart Lane they can clinch a place this time round after stretching their unbeaten league run to 12 matches and moving above Chelsea with 54 points from 28 games.
"It was a very, very important win for us," Spurs manager Andre Villas-Boas told reporters. "There are still 10 matches to go and we have to keep fighting hard to get back into the Champions League, but we are motivated and confident, while Arsenal are at a low."
Arsenal manager Arsene Wenger was puzzled by his team's loss.
"When we went 2-0 down we should have been 2-0 up," he said.
"It was a strange game to lose and it is difficult to understand how we lost it. We made mistakes at the back but they never dominated us and we played very well. Now we have a massive challenge to finish in the top four."
ALL ARSENAL
Arsenal dominated the first 25 minutes, closing Spurs down quickly and looking far more impressive than they had done in many recent matches.
Much of the pre-game hype had centred on Tottenham midfielder Bale, who had been in stunning form with eight goals in his previous six matches, and he continued his prolific form.
The Welshman fired Spurs ahead with his first real chance, narrowly staying onside to collect a through ball from Gylfi Sigurdsson and shoot into the far corner of Wojciech Szczesny's net.
Arsenal's defence was quickly breached again when Scott Parker picked out Lennon who beat the offside trap and waltzed round Szczesny to double the lead.
Arsenal won last season's derby at Emirates Stadium 5-2 after trailing 2-0 and they also trailed 1-0 there this season before beating Spurs 5-2 again and they came back into this match when Mertesacker headed home at the near post from a Theo Walcott free-kick.
But Arsenal's hopes of another fightback were thwarted by the superb Spurs defence in which Jan Vertonghen was outstanding alongside captain Michael Dawson.
"It was massive win today," Daw
