Luke Fletcher took 3 for 44 and Nottinghamshire captain Steven Mullaney 3 for 51 to bowl Derbyshire out for 318, 300 behind the visitors who enforced the follow-on.
That left the Division Two leaders 38 overs to push for victory but Harry Came with 38 and Luis Reece, 30, stood firm to steer Derbyshire to 79 without loss.
Watch day three highlights above.