Devonte Redmond, pictured above, put United ahead on 25 minutes with a penalty, but Lewis Walker’s header levelled the scores after the break for Derby.
A second yellow card for Cameron Cresswell meant United had a man advantage for 18 minutes but could not make it count.
The point keeps them bottom on 12 points. Derby go eighth with 18 points.
Derby: 12 Feb v Nott'm Forest (A) PL Cup
Man Utd: 16 Feb v Chelsea (H) PL2