Goals from Craig Bryson, Tom Ince and former Blue Darren Bent have given Derby a 3-0 half-time lead over Town at Portman Road.
Skipper Luke Chambers, who is staying with the Blues despite interest from his former club Nottingham Forest, started for Town with manager Mick McCarthy making three changes from the team which drew 1-1 at Preston on Saturday.
Paul Digby, Jordan Spence and Kevin Bru came into the side for Josh Emmanuel and Grant Ward, who dropped to the bench, and Toumani Diagouraga, who missed out.
The Blues started in a 3-5-2 system with Chambers in the centre of the defence between Christophe Berra and Paul Digby. Jordan Spence and Jonas Knudsen were the wing-backs.
In central midfield Cole Skuse was partnered by Kevin Bru with Tom Lawrence ahead of them and Freddie Sears and Brett Pitman up front.
Derby were without Blues nemesis David Nugent (knee), midfielder Will Hughes (hamstring) and winger Jonny Russell (knee). Ex-Blues striker Bent started.
After a scruffy start, Derby won a series of corners which eventually led to their opening goal in the ninth minute.
Chambers headed a flag-kick from the right clear, the ball was played back into the right of the box to Ince, who took it down and laid it to Bryson on the edge of the box, from where he struck a low shot past Bartosz Bialkowski to his right.
Within three minutes it was 2-0. Ince brought the ball in from the right unchallenged and smashed a left-footed shot across Bialkowski and into the net, a goal reminiscent of Lawrence’s at Preston on Saturday but from the other flank.
Town switched to a four-man backline as they looked to get back into the game with Digby moving into five-man midfield with Lawrence on the left and Sears the right and Pitman up front on his own.
The Blues threatened for the first time in the 21st minute when Lawrence tricked his way past a couple of defenders on the edge of the box then hit a shot which was too close to Derby keeper Scott Carson.
Town toiled as they sought to get back in the game but Derby created the next opportunity, Abdoul Camara cut the ball back to Ince, whose low shot was too close to Bialkowski.
The Blues were making little headway with Derby happy to sit back and let Town play the ball around unthreateningly at the back. With nine minutes of the half remaining McCarthy switched Digby for David McGoldrick.
On 41 Lawrence made a run towards goal towards the right and hit a shot which was blocked. The loose ball fell to Bru, but his low cross into the area was cut out.
Two minutes later, Bru sent Sears away on the right and the ex-West Ham man won the first of three corners. From the third, Chambers headed into the ground and Carson pawed the ball away from Berra at the far post.
Moments later, Lawrence, Town’s only first-half danger man, turned his ankle as he cut inside a defender and required treatment.
In injury time Ince sent a dangerous ball across the Blues six-yard box, which Chambers turned behind.
And in the aftermath of the resultant corner, the Rams made it 3-0. The ball was cleared to Bryson just outside the area from where he struck a powerful shot which Bialkowski superbly tipped onto the bar.
However, the ball was sent back in from the right and an unmarked Bent nodded into the net from close range with several Town players claiming that the former England striker - who didn’t celebrate against his old club - had fouled Knudsen as the ball came over but to no avail.
Soon after referee Andrew Madley’s whistle ended the half and started a chorus of boos which followed manager McCarthy off the pitch and down the tunnel.
Derby had hardly been made to work for their three goals, the two early strikes having set the half up for them perfectly.
Having got comfortably in front the Rams were happy to sit back and let Town try to find a way through them, which the Blues were wholly incapable of managing with only Lawrence showing any threat at all.
The third goal was just as poor as the other two and made the already very difficult task of getting back into the game all but impossible.
Town: Bialkowski, Spence, Digby (McGoldrick 36), Chambers (c), Berra, Knudsen, Skuse, Bru, Lawrence, Sears, Pitman. Subs: Gerken, Ward, Douglas, Dozzell, Moore, Emmanuel.
Derby: Carson, Baird, Keogh (c), Pearce, Olsson; Johnson, Bryson, Butterfield; Ince, Camara, Bent. Subs: Mitchell, Christie, Shackell, Anya, de Sart, Blackman, Vydra. Referee: Andrew Madley (West Yorkshire).