Andrew Burgess netted twice as Rushden overpowered 10-man Altrincham.
Shaun Densmore was dismissed after 21 minutes for a foul on Yannick Bolasie and Burgess put the visitors ahead soon after with a blistering 30-yard effort.
Lee Tomlin curled in left-footed from the edge of the area shortly before half-time, while after the break Colin Little hit a post for Altrincham.
Curtis Osano made it three from a Tomlin corner and Burgess completed the scoring from Gareth Jelleyman's pass.
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