Luke Rooney's second-half goal was enough to see Luton Town past their replay with Bury and into a third-round tie against Cambridge United.
The sides drew 1-1 last week and there was little between them again as Fraser Franks' header deflected against the Bury post in an uneventful first half.
Rooney's cross just after the break eluded everyone and found its way in.
And the Hatters survived a scare at the death as Nathan Cameron missed with a header from six yards.
The Hatters will now travel to Cambridge on Saturday, 3 January, in what will be their ninth meeting in the past three years.