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