Chesterfield, hit by injury and illness, could find no way back from a start which left them 2-0 down after four minutes.
Oldham took just 47 seconds to grab the lead after Warne's hard work down the left earned them a corner. The kick was floated over by Andy Liddell and defender Guy Branston climbed 10 yards out to head past the stranded Barry Roche.
Less than three minutes later Chesterfield were left stunned again and their wayward defence was punished. Branston got his head to a header across the box and Liddell controlled at the far post before sending a superb volley into the top corner.
Chesterfield finally woke up with Janos Kovacs and Wayne Allison testing home keeper Chris Day.
Oldham's Rob Scott went close just after half time, but Chesterfield gave themselves hope in the 51st minute.
It was a goal created by strike pairing Allison and Colin Larkin who made the most of bad defending by Oldham and Derek Niven, supporting from midfield, slid his shot into the bottom right-hand corner of the net from 12 yards.
Oldham soon regained their two-goal lead thanks to the hard working Warne. A long free-kick was helped on by Branston for Warne to nod home from eight yards.
Chesterfield rang the changes in a bid to salvage something, but Oldham nearly added another when Chris Porter saw his dipping shot just clear the bar.
And they went close again as Warne controlled a Liddell pass and fired inches wide.
Richard Butcher wasted the next chance, but Oldham sealed their win three minutes from time as Delroy Facey crossed and Chesterfield debutant Phil Picken deflected Warne's header into his own net.