Zian Flemming scored the only goal of the game as the Clarets won at Ewood Park for the fifth game on the spin.
Scott Parker’s men, now unbeaten in 13, sit second just a point adrift of leaders Leeds, who were pegged back to draw 3-3 with Hull City.
Elsewhere, Sheffield United beat Watford 2-1 away while Sunderland edged past 10-man Portsmouth 1-0 on Sunday.
Following the weekend’s action, The Football League Paper has collated its Team of the Week, featuring the best performers – here’s the team in full:
1. Max O'Leary (Bristol City)
The stopper kept a clean sheet on Saturday as the Robins edged past Derby 1-0. Photo: Dan Mullan
2. Duane Holmes (Preston North End)
Holmes claimed the assist for Will Keane's equaliser as PNE drew 1-1 with Oxford United. Photo: Matt McNulty
3. CJ Egan-Riley (Burnley)
The centre-back was an absolute rock once again as Burnley kept another clean sheet during their 1-0 derby win against Blackburn. Photo: Molly Darlington
4. Luke McNally (Bristol City)
The former Claret scored Bristol City's winning goal during their 1-0 win against Derby. Photo: Alex Davidson