Jay Rodriguez scored a second-half winner as Burnley edged out Bristol City to make it seven Championship games unbeaten.
Rodriguez headed in a cross from Johann Berg Gudmundsson for his fifth goal of the season midway through the half to secure only a second home win of the campaign for the Clarets, as they moved up to fourth.
For the Robins, Nahki Wells had cancelled out Manuel Benson's early strike.
But they suffered a second loss on the road in four days, having lost 3-2 at Norwich City in midweek, as they fell to eighth in the table.