Adebayor, who had given Spurs a 10th-minute lead against his former club in the Premier League's early kick-off, was shown a red card for a two-footed challenge on Santi Cazorla seven minutes later, and the visitors never recovered.
Germany defender Per Mertesacker equalised for Arsenal with a powerful header after 24 minutes, and Arsene Wenger's side scored twice in the last three minutes of the first half - through Lukas Podolski and Olivier Giroud - to take control.
Spaniard Cazorla made it four from Podolski's cross on the hour, and although Gareth Bale gave Spurs some hope, Theo Walcott rounded off the scoring in injury time as Arsenal produced a repeat of their 5-2 victory over Spurs in February.
"If we show that ambition and courage, we can climb right up the table," Walcott told Sky Sports. "I think we shut a few people up with how good we were today."
Wenger, whose team leapfrogged Spurs into sixth place before the later kick-offs, said: "People are there to question us when we are not at the top but I have great confidence in this team.
"I believe it has something special, and what we want to do now is show it on a consistent basis."
The day ended with Arsenal in high spirits, though the game's opening half-hour - breathless and anxious - reflected the mindset both sides had brought into the contest.
Arsenal, who had wasted a two-goal lead in their previous two games, were trying to deal with their worst start to a season since 1982/83. Tottenham, having beaten Manchester United in September, had just lost two in a row to give the critics of manager Andre Villas-Boas more ammunition.
There is not much a manager can do, though, when one of his strikers attempts to win an innocuous 50/50 ball by diving in with both feet off the ground around the halfway line.
Arsenal fans bayed for blood, and the referee, Howard Webb, showed Adebayor a red card.
Until then Spurs had looked the more threatening.
England forward Jermain Defoe brilliantly turned Mertesacker to latch on to Jan Vertonghen's lofted pass, and although Defoe's side-footed shot was palmed away by Wojciech Szczesny, Adebayor was there to tap the ball into an unguarded net.
Both managers agreed with Webb's decision to send Adebayor off, though Villas-Boas said he had no plans to punish his player. "It was one of those things that can happen," the Portuguese said. "It was a normal situation when a player disputes a ball, there was no intention to do any harm."
Spurs winger Aaron Lennon had a chance to make it 2-0 before Adebayor was dismissed, but thereafter Arsenal responded well.
After Mertseacker's equaliser, Giroud forced two sharp saves from French compatriot Hugo Lloris.
In the 42nd minute, Podolski squeezed home Arsenal's second with a left-foot shot that squirmed off the heel of Spurs defender William Gallas, and just before half-time the excellent Cazorla rode a challenge, burst into the area, and crossed low for Giroud to turn the ball past Lloris.
Cazorla made it 4-1 on the hour before Bale drilled a right-foot shot past Szczesny from 20 metres to give S
