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Rob Hulse grabbed the vital goal against his former club to send Pride Park wild.
Derby held on for a nail-baiting last quarter to secure a morale-boosting win which lifted them off the foot of the Championship table.
The Rams produced their best performance of the season so far to ease the pressure on under-fire boss Paul Jewell and thoroughly deserved the points.
They took the lead on 24 minutes when Paul Green headed home a Kris Commons left-wing cross.
Within two minutes, the Blades were back on terms as Darius Henderson rose unmarked at the far post to head home Greg Halford's right-wing cross.
Derby thought that they should have had a penalty on 55 minutes when Hulse was brought down in front of referee Chris Foy.
The official seemed to give the spot-kick only to change his mind after consulting his assistant.
The disappointment for Derby was forgotten when Hulse rifled home his 70th minute winner by converting Nacer Barazite's right-wing cross.