Second-half goals from Lucas Akins, Luke Freeman and Filipe Morais saw Stevenage end Stourbridge's cup run with a 4-0 win.
Team news for Saturday's FA Cup second-round clash between Stevenage and Stourbridge at Broadhall Way.
Stevenage boss Graham Westley said his players had lost their "appetite" following a 3-1 home defeat to Shrewsbury.
Tom Eaves marked his return to Shrewsbury with a goal in their 3-1 victory at fellow strugglers Stevenage.
Team news for Saturday's League One clash between Stevenage and Shrewsbury at Broadhall Way.
Graham Westley blamed fatigue for his Stevenage's "lacklustre" performance in their 3-2 defeat at fellow strugglers Gillingham.
John Mousinho's first goal for Gillingham gave them a crucial 3-2 home victory at the expense of his former club Stevenage.
Team news for Tuesday's League One clash between Gillingham and Stevenage at Priestfield Stadium.