Shefki Kuqi scored the only goal in the 66th minute but the match will be remembered more for the red cards shown to Derby's Jay McEveley and Swansea's Gorka Pintado.
Swansea came into the game unbeaten in ten League matches and started well but it was Derby who carved out the first opening after nine minutes.
Kris Commons carried the ball across the pitch and Paul Green slid Rob Hulse in but his shot from ten yards was blocked by Dorus de Vries.
Swansea had to make an early change when midfielder Andrea Orlandi went off in the 15th minute but Derby lost Commons ten minutes later with a hamstring problem.
The rest of the first half was a tepid affair but the game came to life in the second period as both teams had a man sent off.
McEveley was the first to go in the 64th minute for a second yellow card when he clearly pulled Nathan Dyer over out on the right and, from the resulting free-kick, the visitors scored.
David Cotterill's kick was flighted to the back post where Kuqi glanced a header inside the right-hand upright.
But five minutes later, Swansea lost their man advantage when Pintado went through the back of Robbie Savage near the right corner flag sparking a mass melee.
Referee Steve Tanner had no alternative but to show a red card but took no further action against any other players after order was restored.
Derby had hardly threatened the Swansea goal but, a minute from the end, Michael Tonge rattled the bar with a 25-yard free-kick but that was the closest Derby came as their four-match unbeaten League run came to an end.