Resuming on 78 for 1, Hamish Rutherford and Chesney Hughes shared a 41 run partnership for the second wicket before Rutherford, driving at Graham Wagg, edged behind to Mark Wallace.
Michael Hogan bowled an excellent opening spell, with Hughes fortunate to survive as he repeatedly played and missed at the Glamorgan seamer.
Wayne Madsen then joined Hughes and the third wicket pair survived until lunch with Derbyshire trailing. Hughes was undefeated on 49 and Madsen 33.