Matthew Kilgallon's header maintained Sheffield United's unbeaten start to the Championship season while ending Derby's 100% record at Pride Park.
The defender nodded Keith Treacy's free-kick past Derby keeper Stephen Bywater with 10 minutes remaining.
Treacy wasted three chances early on before former Blades striker Rob Hulse volleyed over from 12 yards for Derby.
After the break, Hulse headed straight at Blades keeper Mark Bunn before nodding a Kris Commons' corner wide.
United's goal came against the run of play after Shaun Barker had fouled Stephen Quinn and Kilgallon rose to nod in Treacy's free-kick.
The visitors should have doubled their lead in stoppage time, but Jamie Ward's shot was superbly saved by Bywater.
Derby manager Nigel Clough:
"We were heading for 0-0 with 10 minutes to go and it was an absolutely ludicrous free-kick to give away near the corner flag.
"The ball ends up ricocheting in off (Rams striker Rob)Hulse but if you don't give free-kicks away the threat doesn't exist.
"I am very disappointed in the manner in which we conceded the goal because we probably did enough to get a point.
"We are losing our voices week in and week out, before games and during games saying don't give free-kicks away, especially in those areas. We are contributing too much to our own downfall."
Sheffield United manager Kevin Blackwell:
"I cannot praise the lads enough.
"We had the end of last season to deal with and I am really pleased with the way they have acquitted themselves.
"It's normally traumatic to lose in the play-off final and many teams struggle the following season but we have put down a good marker and set off at a good pace and I think it's all credit to the players."
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