A slow first half burst into life in the second period at Ashton Gate, as Nathan Baker's sending off saw Blackburn Rovers take full advantage to record a 2-0 win.
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The biggest chance of the first half fell to Hope Akpan after 32 minutes but the midfielder's effort from a rebound was cleared off the goalline.
On-loan Aston Villa defender Baker, who was booked in the opening period for hacking down Tom Lawrence, was given his marching orders in the 49th minute for another foul on the forward.
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Paul Lambert's side made the most of their numerical advantage with 59 minutes gone, as Grant Hanley netted from a set piece.
Conway's corner found Lawrence at the back post, his ball into the box was headed down by Duffy for Hanley to side-foot home.
Rovers doubled their lead from the spot in the 87th minute to put the tie beyond doubt.
Marcus Olsson was taken down inside the area to hand Ben Marshall the opportunity from 12 yards, the midfielder making no mistake with his penalty.
Rovers move up a spot in the Championship table to 13th, while the Robins fall one place to 21st.
