Derby may have harboured remote hopes of making it two Premier League wins in a row, but their quest was dented by Abou Diaby after just ten minutes when he smashed home a 25-yard drive into the top right corner of the net beyond the dive of Stephen Bywater.
The Derby keeper was able to deny the Gunners two minutes later when Diaby fired in a well struck low drive that Bywater managed to parry with the follow up shot from Theo Walcott flying wide.
The Gunners had a good claim for a penalty on 15 minutes when the fleet-footed Walcott was bundled down in the area by Claude Davis, but referee Martin Atkinson, who was considerably behind play, waived the claims away.
Adebayor doubled Arsenal's lead on 25 minutes when he accelerated on to a defence splitting ball from Cesc Fabregas before rounding Bywater and slotting the ball into a vacant net from an acute angle.
Walcott almost added another just before half-time when he accelerated on to a clever Fabregas reverse pass.
The young Gunner fired a shot from the right side of the area that stopped short of crossing the line having clipped the inside of Bywater's legs on its way.
The Derby keeper also denied Eduardo in first-half injury-time when, at full stretch, he parried the striker's well-placed header.
Derby went further behind just four minutes after the re-start when Eduardo was hauled down by Matty Oakley inside the area.
Up stepped Adebayor to take the spot-kick and he coolly placed the ball into the bottom right corner of the net beyond Bywater's despairing dive.
Fabregas made it 4-0 on 70 minutes with another thunderous strike from distance after Eduardo had teed him up on the right corner of the Derby area.
Adebayor then completed his hat-trick to put the Gunners 5-0 up on 79 minutes.
The Togo striker showed great strength to control a long ball from Denilson on his chest, before turning to dispatch a low shot that Bywater could only help on its way into the net.
Derby tried changing things around and brought on fans' favourite Giles Barnes, but they could not get near the Gunners who kept possession well to secure the points and move further ahead of the chasing pack.