League One opponents Oldham created early chances, with Adam Rooney and Jonson Clarke-Harris both missing the target from close range.
But Derby hit the bar through a Michael Jacobs header and it was Jacobs who grabbed what proved to be the winner after 20 minutes, sweeping in from six yards after a left-wing cross by Conor Sammon.
Oldham goalkeeper Mark Oxley made a flying save from Jeff Hendrick before Rams shot-stopper Lee Grant denied Clarke-Harris and Cristian Montano either side of half-time.
Derby wasted an excellent chance to double their lead when the unmarked Ben Davies headed wide at the far post at Boundary Park.
Gallant Oldham thought they were level after 74 minutes, but Montano's shot was brilliantly cleared off the line by Craig Forsyth.