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Gareth McAuley and Carlos Edwards put the visitors in control, but Rob Hulse replied before first Derby boss Nigel Clough was sent to the stands and midfielder Stephen Pearson was red carded for dissent.
Connor Wickham wrapped up a deserved victory that gives manager Roy Keane a double over Clough, a former team-mate at Nottingham Forest.
Ipswich could not have asked for a better start after McAuley fired them into a fourth-minute lead.
Jack Colback's corner was met by a Jonathan Walters header which was blocked, but McAuley drove the rebound into the roof of the net.
Derby's play was disjointed but they had a good chance to equalise in the 28th minute when Pearson headed back across goal but Chris Porter was closed down before he could shoot.
Ipswich went close to a second three minutes later when Daryl Murphy was unmarked at the back post and it needed a sharp save from Stephen Bywater to keep out his low shot.
Murphy was only inches away from scoring in the 35th minute when Wickham drove the ball through a crowded six-yard box but the striker just failed to connect.
Derby were denied an equaliser in the 42nd minute when Shaun Barker headed powerfully towards the top left corner only for Brian Murphy to claw the ball away
Murphy was fortunate four minutes into the second half when he raced out to try and collect a long ball but was beaten to it by Barker whose header bounced wide.
Derby had another good chance to score in the 56th minute when Steve Davies crossed from the left but Pearson headed into the arms of Murphy from six yards.
Ipswich were coming under increasing pressure but Colback almost put them two up with a 20-yard shot that Bywater did well to parry to his left.
Rob Hulse headed a Robbie Savage cross wide, before on-loan Wigan striker Tomasz Cywka made his Derby debut with 12 minutes left.
But the visitors hit Derby with a breakaway goal nine minutes from the end when Wickham crossed low from the right and Edwards bundled the ball in.
Derby replied immediately when Hulse headed in a Savage cross but manager Clough was then sent to the stands by referee Jonathan Moss, who then red carded Pearson for what appeared to be dissent.
Wickham ended any chances of a Derby recovery in stoppage time when he got away from Jay McEveley to slide the ball past Bywater for his first goal since signing a two-year contract.