Their bowling attack struggled as Wayne Madsen (32no) and Paul Borrington (30no) sensibly saw Derbyshire through to lunch before the weather turned severe and play was stopped.
Second placed Yorkshire earned three bonus bowling points as they tore through the Sussex attack to leave them 276 for nine.
Ryan Sidebottom was the pick of the bowlers, taking three wickets, as Liam Plunkett and Kane Williamson took two each.
Middlesex’s title hopes suffered a blow against Nottinghamshire as they took just two wickets, with Steven Mullaney (88no) proving particularly hard to shift, before rain ended proceedings early.
Scores: Day One
Derbyshire 99/1 v Durham
Essex 186/4 v Kent
Lancashire 92/0 v Leicestershire
Nottinghamshire 161/2 v Middlesex
Surrey 195/8 v Somerset
Sussex 276/9 v Yorkshire
Hampshire 197/3 v Worcestershire