Patrick Bamford’s opening minute goal sees Derby leading the Blues 1-0 at half-time at Portman Road.
Town boss Mick McCarthy named the expected unchanged side with Anthony Wordsworth again replacing the injured Cole Skuse in the centre of midfield.
Derby made one change from the side which started the 5-0 thrashing of Nottingham Forest at the weekend with Johnny Russell replacing the injured Jamie Ward.
The Rams went ahead with their first chance of the evening with the game only 33 seconds old. After breaking following a Town attack, Craig Forsyth cut the ball back from the left and Bamford swept home from the edge of the six-yard box.
Having gone behind so early the Blues put on a brief spell of pressure but were unable to create an opportunity. On 12 Jeff Hendrick’s through ball almost played Craig Bryson in on goal but Town keeper Dean Gerken was off his line quickly to claim.
Former Norwich man Chris Martin was booked in the 15th minute for shoving over Christophe Berra after the Scottish international had remonstrated with the Derby striker for going to ground very easily on the edge of the box.
Wordsworth saw a shot blocked in the 20th minute but the Blues — with Stephen Hunt now on the right and Paul Anderson on the left - were still to create a serious chance, while the Rams were continuing to look dangerous on the break, goalscorer Bamford cutting in and hitting a low 26th minute shot to Gerken.
On 28 Martin was very fortunate not to receive a second yellow card for a late challenge on Berra, referee Fred Graham waving away the Town protests much to the annoyance of the home support.
Moments later, Russell sent a low ball across the Blues’ six-yard box but with none of his team-mates far enough forward to take advantage.
Derby keeper Lee Grant was having a quiet evening with claiming a Jonny Williams cross his biggest test during the first half.
In injury time the Rams were again very lucky not to see their number reduced when Bryson caught Williams with a very high challenge midway inside the Blues half, the on-loan Crystal Palace man requiring lengthy treatment, not for the first time during the first period. Referee Graham showed only a yellow card.
The Wales international appeared to have been targeted by the Rams and soon after the game restarted was fouled again, albeit less severely, this time by Hendrick, who escaped a card.
Referee Graham blew his whistle moments later and was booed off the field by an increasingly incensed home crowd, while Mick McCarthy made his feelings known to the official as he made his way towards the tunnel.
After conceding so early, the Blues had had a fair amount of possession but without creating any significant chances with Derby closing them down quickly.
The Rams, who could count themselves very fortunate to end the half with 11 men, attacked slickly and with pace when they had the ball.
Town: Gerken, Chambers, Berra, Smith, Cresswell, Anderson, Hyam, Wordsworth, Hunt, Williams, Murphy. Subs: Loach, Mings, Richardson, Tabb, Green, Ebanks-Blake, Nouble.
Derby: Grant, Wisdom, Keogh, Buxton, Forsyth, Thorne, Bryson, Hendrick, Russell, Bamford, Martin. Subs: Legzdins, O'Brien, Whitbread, Bailey, Naylor, Sammon, Thomas. Referee: Fred Graham (Essex).