Two late goals gave Arsenal a 2-0 win in an eventful local derby at West Ham.
The Hammers Carlton Cole was then dismissed in the dying seconds for a late tackle on Alexandre Song.
Gunners boss Arsene Wenger told Sky Sports: "I believe we took the initiative and they played on the counter-attack, but we did not make any big mistakes defensively.
"From then on it was a question of patience and we knew that if we could keep the tempo high we would have chances in the last 20 minutes. And that's what happened."
The Frenchman conceded that Adebayor's contribution was decisive.
"I believe he came on with a determined attitude and he did very well today."
Wenger also expressed his satisfaction with Arsenal's start to the season.
"In October I believe that is a good position to have but let us not focus too much on our opponents but rather ourselves.
"We want to keep winning and that is more important."