Aidy Boothroyd hailed a 'massive, massive' result and a second clean sheet in succession as Lee Collins and debutant Stuart Dallas scored the goals for his men.
Town now travel to face an Oxford United side whose home defeat at the hands of Southend United on Saturday means they have just one victory in the league at the Kassam Stadium this season despite remaining in the League Two play-off places.
"We need to be better collectively, individually and to produce what we produce through the week on the training ground when we play at home," said manager Chris Wilder.