A hard-fought encounter at Turf Moor was settled by Sam Vokes' goal midway through the second half to ensure that the home side continued their push towards promotion.
Dougie Freedman's side again showed how difficult they are to break down but the Reds could not find a way back into the game after Vokes' strike and are now in 12th place in the Championship after a win for Brentford at home to Wolves.
Saturday sees a return to the City Ground and a home game against a Bristol City side who were heavily beaten at home by Brighton on Tuesday evening.
Speaking to the official club website after the game, Freedman said: "I felt they were the better side in the first half, we defended very well to keep it 0-0, but in the second half I felt we were the better side.
"We controlled the game defensively and on the ball we were fantastic."