Half-time substitute Adebayor scored three times in half an hour to put the game beyond the home side with Theo Walcott also getting on the scoresheet, while Robert Earnshaw scored his first Premier League goal for the home side.
The result keeps Arsenal’s paper-thin hopes of winning the title alive, although it will take an extraordinary occurrence for them to finish above Chelsea and Manchester United with only two games remaining.
Pride Park was a fitting venue for a game where pride was the only thing at stake, with Derby long since relegated and Arsenal’s title ambitions dependent on mathematical improbabilities.
Arsenal threatened first when Kolo Toure sent an acrobatic volley over the crossbar from Bendtner’s left-wing cross after five minutes, but it was the home side who began the most strongly, attacking with a vigour that belied their basement status.
Villa then had a powerful header diverted behind by William Gallas, before the visitors took the lead against the run of play thanks to the kind of glaring defensive error that has blighted Derby’s season.
Van Persie could, and should, have made it 2-0 shortly afterwards when he sidefooted wide after being set up by Walcott, and Derby made him pay for his profligacy by equalising minutes later.
McEveley attacked Robbie Savage‘s free-kick from the left, and when the ball fell in front of him after glancing off his head he reacted quickly to stab it past Premier League debutant Lukasz Fabianski from close range.
The goal drew a rapturous reaction from the home fans, but gradually Arsenal imposed themselves, and they took the lead for a second time six minutes before the break when van Persie took Toure’s clipped pass on his chest before slamming the ball past Carroll with his right foot.
Van Persie was forced to withdraw with a tight hamstring at half-time, with Adebayor replacing him, but in passing, movement and quality of football it was a far more familiar Arsenal that took to the field for the second half.
Toure twice shot over – the second time after being set up by a lovely backheel from Cesc Fabregas – before Carroll saved with his feet from Adebayor.
The Togolese international would not be denied though, and just before the hour mark he increased Arsenal’s lead, tapping home at the back post after Emmanuel Eboue had helped on Walcott’s cross from the right byline.
A two-goal cushion established, the visitors really began to turn on the style, with Walcott shooting wide after being put clean through by Bendtner, before Derby substitute Earnshaw threatened an unlikely comeback by reducing the deficit with a neat finish after Andy Todd‘s pass had sliced the away defence in two.
But it proved a temporary reprieve. Walcott bent a shot past Carroll to restore Arsenal’s lead, before Adebayor claimed his second with a close-range finish from Gael Clichy‘s left-wing cross.
Derby continued to pour forward, even as their fans began to leave the stadium, but Adebayor delivered the final blow in injury time when he raced clear of the home defence before rounding Carroll and tucking the ball into the empty net to claim the match ball.
Tom Williams / Eurosport