Jamie Mackie and Darius Henderson were paired up front for Forest in Billy Davies' starting XI but it was un unlikely goal source who proved to be the difference between the two sides.
Defender Jack Hobbs headed home from Andy Reid's corner with 5 minutes to go to half-time after an opening 45 minutes in which both sides had looked dangerous going forward.
The second-half saw chances at both ends as the game opened up after the break and Forest wasted a golden opportunity to wrap things up when Henderson's penalty was saved by Grant after a foul that saw Rams defender Richard Keogh dismissed.
A late flurry from the visitors was kept at bay as goalkeeper Karl Darlow was called into action and the Reds were able to celebrate a hard-fought win against their great rivals.
28,276 watched the game at the City Ground with Forest returning to the automatic promotion places ahead of the 3pm kick-offs.
***Update*** The defeat marked the end of Nigel Clough's reign as Derby manager, one that begun in January 2009.
"After much consideration, the board feel it is time to move Derby County forward to the next level," said a club statement.
"The club would also like to take this opportunity to wish Nigel Clough well."
The former Forest striker had expressed himself pleased enough with Derby's display at the City Ground, saying: "I thought we were very good."