The result extended Bradford’s run of home matches without a win to six, going back three months, and means they have lost their last six league and cup matches against Rotherham.
After a frantic start, the visitors went in front after 20 minutes when the Bradford defence failed to clear after a surging run from Lee Frecklington. The ball fell to Newcastle loanee Vuckic, who scored with a superb shot into the far corner from just inside the penalty area.
The home side rarely looked like saving the game in the second half and it needed two fine saves from Jon McLaughlin to prevent James Tavernier from increasing Rotherham’s lead.
First, McLaughlin turned away Tavernier’s free-kick from from the the edge of the penalty area in the 48th minute and then made a diving save to deny the same Rotherham player in the 65th minute.
The only serious save Rotherham keeper Adam Collin had to make was to keep out a first-half effort from Garry Thompson.