The Gunners, 5-0 winners at the Emirates earlier in the season, were fortunate to lead 2-1 at the break after goals from Nicklas Bendtner and Robin Van Persie either side of a Jay McEveley effort.
But the second half belonged to the Togo international who struck three times to take his season's tally to 30 - which include three in September's clash between the teams in north London.
Rams record signing Rob Earnshaw grabbed his first league goal for the club, while Theo Walcott was also on target in an eight-goal thriller.
Earnshaw's effort had Derby just 2-3 behind - but then Arsenal took charge with Adebayor and Walcott firing them clear of the cellar-dwellars.
The Gunners are now third on the table with 76 points, four points behind joint Premiership leaders Manchester United and Chelsea, with two games to play.