Schoolboys pipped in first-half goal rush
They took an early lead through Ryan Doxey but Derby quickly levelled. However Zac Hinch regained Rotherham's lead only for Derby to cancel his strike with a second goal of their own.
Hinch was on target again minutes later to give Rotherham a 3-2 advantage but Derby equalised for a third time before grabbing their fourth minutes before the break.
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Hide AdKing Edward VII School (Sheffield) have landed a home tie against Heckmondwike Grammar in this season's ESFA Under-18 Schools' Trophy for Boys first round.
High Storrs (Sheffield) entertain Cardinal Langley RC Sports College (Manchester).
Balby Carr Community Sports College, also at home, to Beckfoot School from Bingley.
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