A 90th-minute strike from Conor Sammon snatched all three points for the hosts after Middlesbrough had rallied with 10 men.
The visitors were dealt a blow shortly after the half-hour mark when Curtis Main was sent off for a second bookable offence, before Chris Martin put Derby ahead on the stroke of the break, heading home Craig Bryson's cross.
Dean Whitehead looked to have earned Middlesbrough a share of the spoils by driving an effort home from close range after 74 minutes, but Sammon had the final say to give Derby a fourth win in a row.
Meanwhile, at Elland Road, Ross McCormack scored twice as Leeds United returned to winning ways with a 2-0 victory over managerless Wigan Athletic, who have now lost three Championship matches in a row.
The Scot set the ball rolling in the 15th minute when he nodded home from a Tom Lees header following a corner.
And he made sure of the three points 13 minutes from time, curling home a free-kick, with Jason Pearce leading the celebrations having initially appeared to have got a touch in the box, before the goal was eventually awarded to McCormack.
Leeds now climb to seventh, just two points short of the play-off places, while Wigan drop to 14th.
In League Two, Anthony Stewart scored in the fifth minute of stoppage time to rescue a 2-2 draw for Wycombe Wanderers at Portsmouth.
In a game that had originally been attempted in October before being suspended in the 46th minute due to a waterlogged pitch, the hosts at Fratton Park - still without a manager following the departure of Guy Whittingham - were behind after 23 minutes thanks to Matt McClure's strike.
Goals from Andrew Barcham and Patrick Agyemang in the space of 11 minutes appeared to have turned the match on its head and sealed three points for Portsmouth, before Stewart earned a point deep into added time.
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