But it all changed in the 40th minute.
Bacary Sagna planted home a header to make it 2-1 and all of a sudden, everything changed.
Robin van Persie levelled it before half-time and within 25 minutes, we were 5-2 down and out of it.
To add insult to injured pride, Scott Parker was sent off for a second bookable offence in the final minute.
Harry Redknapp made just one change to the team that beat Newcastle so impressively in our last Premier League outing as Younes Kaboul came in for Michael Dawson, partnering Ledley King in central defence.
Kaboul and King were joined by Brad Friedel, Luka Modric, Benoit Assou-Ekotto, and Adebayor in the line-up, all returning after they sat out the FA Cup draw at Stevenage last weekend.
It took just four minutes to open the scoring as Adebayor spotted Louis Saha in acres centrally, the striker shifted onto his left foot and his shot clipped off Thomas Vermalen, looped over Wojciech Szczesny and home.
Adebayor headed wide and Kranjcar looped a header onto the roof of the net as we looked a constant threat on the break.
Arsenal looked capable in the final third though and it took a fine save from Friedel to tip over Tomas Rosicky's glancing header in the 22nd minute.
The second goal came as Modric released Bale, he sped between Kieran Gibbs and Vermaelen and was brought down by a combination of Gibbs and Szczesny.
Referee Mike Dean pointed to the spot - no card - and after a delay, Adebayor did the rest from 12 yards.
Szczesny saved well from Bale as we looked to build on our lead, but it all changed on 40 minutes.
Van Persie struck the post but Mikel Arteta clipped the ball back in for Sagna to head home for 2-1.
It was soon 2-2 as Van Persie made something out of nothing, picking up a poor clearance, making space and curling beyond Friedel from 22 yards.
Half-time arrived and the theory was that we would come firing back into it in the second half, and Harry made two changes, Rafa van der Vaart and Sandro replacing Saha and Kranjcar.
But there was no time to get a foothold back in the game as Rosicky managed to turn home Sagna's cross at the near post for 3-2 after 51 minutes.
Theo Walcott fired just wide and then latched onto Van Persie's pass and clipped calmly over the advancing Friedel for 4-2 on 65 minutes.
Three minutes later and it was all over as Alex Song's pass released Walcott and he drilled across Friedel into the far corner.
We managed to fire in a couple of shots from distance and Szczesny did well to hang onto Sandro's deflected effort, but the only other action of note was Parker's sending off for a second yellow card a minute from time.
Arsena (4-3-3)l: Szczesny; Sagna, Vermaelen, Koscielny, Gibbs (Jenkinson, 75); Song, Arteta, Rosicky; Walcott (Oxlade-Chamberlain, 81), Van Persie, Benayoun (Gervinho, 89). Unused subs: Fabianski, Park, Chamakh, Miquel.
Spurs (4-4-2): Friedel; Walker, Kaboul, King (Dawson, 81), Assou-Ekotto; Kranjcar (Sandro, 46), Modric, Parker, Bale; Adebayor, Saha (van der Vaart, 46). Unused subs: Cudicni, Rose, Lennon, Defoe.
Goals: Arsenal - Sagna (40), Van Persie (42), Rosicky (51), Walcott (65, 68). Spurs - Saha (4), Adebayor (penalty, 33).
Referee: Mr M Dean.
When Emmanuel Adebayor slotted home a penalty to make it 2-0 in the 33rd minute we looked nailed on to complete the double over our neighbours and further boost our third spot in the Premier League.