Lee Frecklington's double helped Rotherham into the next round, despite a sterling comeback from Stevenage.
Kari Arnason set up Mark Bradley to open the scoring for the Millers.
Frecklington scored with a long-range effort after Ben Pringle's pass, before picking up a loose ball two minutes later and adding another.
James Dunne's 30-yard strike gave Stevenage hope before Filipe Morais scored after Marcus Haber's shot was saved, but Rotherham held on.
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