Stuart Gray's first-half penalty gave Rushden & Diamonds their passage into the second round of the LDV Vans Trophy with victory at Oxford.
Gray thumped home his spot-kick nine minutes before half-time after Rodney Jack was brought down in the box by Jon Ashton.
But Oxford produced a battling second-half performance and made the Second Division side work hard for it.
David Bell and substitute Andy Burgess both missed open goals that would have given Rushden some breathing space.
Diamonds keeper Paul Evans made sparkling saves in the second half to keep out efforts from Jefferson Louis and Danny Brown.
Oxford Utd: Woodman, Ashton, Crosby, Bound, McNiven, Townsley,
Waterman, Brown, Robinson, Hackett, Louis.
Subs: Brooks, Cox,
Whitehead, Wanless, Omoyinmi.
Rushden & D'monds: Evans, Bignot, Edwards, Dempster, Underwood,
Mills, Bell, Hanlon, Gray, Jack, Kitson.
Subs: Darby, Burgess,
Sambrook, Story, Hall.
Referee: L Probert (Gloucestershire).