Derbyshire made it two goals in two games for the Latics after Clarke scored for the third straight match to give Scunthorpe the lead.
Alan Knill's side struck within three minutes when Mark Duffy picked out Clarke, who turned sharply and drilled inside the far post from 10 yards.
Derbyshire forced a save from keeper Sam Slocombe, but Scunthorpe went close through Christian Ribeiro, Jimmy Ryan and Karl Hawley.
Oldham stopper Dean Bouzanis made a fine save from Hawley and the Latics pulled level five minutes before half-time as Jonathan Grounds' left-wing cross was bundled in by Derbyshire from six yards.
Clarke missed a golden chance to restore the Scunthorpe lead, but Slocombe did well to save Matt Smith's header down by a post.
Oldham were denied a stoppage-time decider when Robbie Simpson headed in but was penalised for a foul on Slocombe.