A second-half penalty from John Nutter kept alive Stevenage's play-off hopes.
He slotted into the net after Chris Hope had fouled Mitchell Cole as Rushden slumped to their fourth consecutive defeat.
Adam Miller went close for Stevenage before Rushden's Danny Williams headed narrowly wide and Lee Tomlin shot straight at keeper Alan Julian.
Paul Hakim drilled a left-footed strike against the Rushden post late on but Nutter's spot-kick was enough.
Stevenage: Julian, Fuller, Nutter, Gaia, Henry, Miller, Cole, Dobson (Nurse 59), Beard (Stuart Lewis 46), Oliver (Hakim 79), Morison.
Subs Not Used: Potter, Guppy.
Booked: Beard.
Goals: Nutter 62 pen.
Rushden & D'monds: Baker, Ashton (Albrighton 46), Watson, Hope,
Hatswell (Beardsley 90), Savage, Mills (Lambley 55), Shaw, Williams, Rankine, Tomlin.
Subs Not Used: Tynan, Wright.
Booked: Tomlin.
Att: 1,715
Ref: A Halliday (West Yorkshire).