Thomas Vermaelen scored in stoppage time, completing the team's fourth straight come-from-behind win in the league.
Adebayor walked off the pitch the star man, scoring one and providing four assists.
Clint Dempsey became the first American to score a hat-trick in the English Premier League.
Craig Bellamy scored twice for Liverpool and substitute Steven Gerrard netted another in a 3-1 win.
Newcastle United beat Stoke City 3-1 to remain unbeaten in the Premier League.