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In the opening 15 minutes, Chesterfield managed to stem the free-flowing attacking play that has seen Derby rise to the upper echelons of the Championship this season.
Jay O'Shea then came close with a long-range effort before the midfielder stung the hands of Roos with a strike from a similar distance just moments later.
The League One side continued to pen Derby inside their own half and Eoin Doyle almost flicked home a cross at the near post, only to see his effort fly inches over the crossbar.
Bent almost doubled his tally early in the second half but Tommy Lee thwarted the former England international.
Simon Dawkins rattled the bar with a header 20 minutes from time, but Derby came under significant pressure as Chesterfield threw bodies forward in search of a leveller.