A second-half double from Kris Commons gave Derby a first win at Portman Road in seven games.
The Rams' leading scorer put the visitors in front with a heavily deflected free-kick just short of the hour and then extended the lead with a cool finish 15 minutes from time.
Blues had chances in an entertaining game and it took terrific saves from Frank Fielding to deny Tamas Priskin and Jason Scotland.
Roy Keane made one change to the side that beat Sheffield United at the weekend, Connor Wickham coming in for his third start of the season, Jason Scotland dropping to the bench.
Jack Colback fired over the bar inside the first minute following a Carlos Edwards cross as Blues looked for an early breakthrough for the third successive game.
Tomasz Cywka responded, forcing Marton Fulop into a fingertip save while at the other end Priskin showed the confident form he is in by testing Fielding in the Rams' goal from 30 yards.
Wickham sent a left footer into the sidenetting as the game flowed, Colback blasting just wide after skipping past two Rams players in midfield.
Grant Leadbitter powered another effort just over as Blues just edged the opening stages, Priskin's header from six yards going straight at Fielding.
Livermore smashed a volley over after a corner had been cleared to the Tottenham loanee on the edge of the box, Colback's cross then just failing to find a blue shirt.
The best chance of the first-half fell to Derby though on the half hour, Livermore's headed back pass intercepted by Shefki Kuqi but the former Town frontman failed to get good contact on his shot and Fulop clawed the ball to safety.
Leadbitter danced around Fielding in the Derby box but his shot was hacked clear, Wickham dragged his shot wide before Fulop came to Town's rescue again with a brilliant save to keep out James Bailey's close range effort.
An equally good piece of defensive work from Gareth McAuley stopped Kuqi getting on the end of Cywka's cross, Commons then showing great skill to cut inside the Blues' defence and test Fulop from 20 yards.
Damien Delaney cut out the threat of Commons again with a timely interception as an even and highly entertaining half came to an end.
Priskin was denied inside the Derby box after his perseverance won him possession, Tommy Smith then doing well to clear from Paul Green as the second-half continued as the first finished, both sides creating openings.
Dean Moxey picked up the first yellow card of the game for a foul on Priskin, Derby dealing with Leadbitter's free-kick. Colback then cautioned for a foul on Green.
The Rams got the breakthrough just before the hour, Commons' 25 yard free-kick taking a wicked deflection to beat Fulop.
Blues were almost level a minute later, Fielding brilliantly saving from Priskin's powerful strike 10 yards out, Town then making a change with Jason Scotland on for Livermore.
Town had two penalty shouts turned down inside a minute, Scotland and Wickham both going down inside the box but referee Roger East waved away the appeals.
Andros Townsend and Jaime Peters were introduced for the last 20 minutes, Edwards and the injured McAuley making way.
Fielding held firm from Scotland's drive before Commons became the third player to be booked, the former Forest player bringing down Townsend.
Kuqi made way for Miles Addison on 73 minutes, Leadbitter then joining the names in referee East's notebook and picking up a one match suspension after taking his tally to five yellows for the season.
The Rams extended their lead 15 minutes from time, Commons stroking the ball past Fulop from Moxey's cross.
Commons was replaced by Stephen Pearson two minutes after his goal as the Rams looked to shore up their lead.
Town were inches away from pulling a goal back on 80 minutes, Moxey heading off the line, Bailey then booked for dissent.
Fielding saved brilliantly again, this time from Scotland as Blues looked for a way back into the game.
Peters joined the card collection for a foul as Derby broke looking to seal the points.
Mark O'Brien replaced Ben Pringle for the final exchanges and there was still time for Fielding to keep out Leadbitter, the England U21 international playing his part in ensuring the points went home with the visitors as Town's three match winning run came to an end.
Town: Fulop, Eastman, McAuley (Peters 68), Delaney, Smith, Edwards (Townsend 68), Leadbitter, Livermore (Scotland 60), Colback, Wickham, Priskin. Subs not used: Murphy, Murray, Kennedy, O'Dea. Booked: Colback, Leadbitter, Peters.
Derby: Fielding, Green, Brayford, Barker, Moxey, Cywka, Savage, Bailey, Pringle (O'Brien 86), Commons (Pearson 77), Kuqi (Addison 73). Subs not used: Deeney, Roberts, Martin, Doyle,. Booked: Moxey, Bailey.