The Rams were cruising to their first home win of the season thanks to Morten Bisgaard's solo effort and an Inigo Idiakez penalty in the first half.
But the home side almost paid the price for relaxing too much as Jerome, who had missed a first-half sitter, hooked home Neal Ardley's cross on 82 minutes.
Derby almost restored their two-goal lead at the end when Marcus Tudgay's shot from outside the box hit the post.
Cardiff boss Dave Jones:
"We're trying to change the whole football club around in five weeks and that's not really going to happen.
"We have got to be patient and keep working at it. If people lose their heads and start feeling sorry for themselves then it's not going to work.
"We're not the first club that's had to change things, and make no mistake, it's been a big, big turnaround.
Derby: Camp, Edworthy, Davies, Michael Johnson, Jackson, Bisgaard (Tudgay 71), Thirlwell, Bolder, Idiakez, Smith (Seth Johnson 84), Rasiak.
Subs Not Used: Grant, Mills, Peschisolido.
Booked: Thirlwell, Bolder, Idiakez, Jackson.
Goals: Bisgaard 21, Idiakez 45 pen.
Cardiff: Alexander, Darlington, Purse, Cox, Barker, Ardley, Whitley, Koumas, Cooper (Boland 57), Jerome, Parry (Lee 46).
Subs Not Used: Margetson, Loovens, Mulryne.
Booked: Purse, Parry, Boland, Cox, Whitley, Lee.
Goals: Jerome 83.
Ref: T Kettle (Rutland).