Max Holden made a career-best 76 before being dismissed as the visitors were all out for 307 before lunch.
The hosts started slowly during a rain-affected afternoon, which saw Northants seamer Ben Sanderson limp off.
Godleman (69) and Reece (63) stood firm to build a lead of 116 runs as they closed on 142-0.
The Derbyshire openers have been patient, facing 152 and 162 balls respectively as they have taken the sting out of their opponents, and as a lack of swing deterred the visitors.
The home side may be tempted to offer Northants a run-chase tomorrow in an attempt to avoid what otherwise appears to be heading for a draw.
Derbyshire openers Luis Reece and Billy Godleman hit unbeaten half-centuries as the hosts assumed control at home against Northants on day three.