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:
5. Bashir Humphreys (Burnley)
The left-back bagged another assist for the Clarets as he provided the cross for Zian Flemming's header during the 1-0 derby win. Photo: Molly Darlington
6. Calum Chambers (Cardiff City)
The former Arsenal man scored Cardiff's equaliser as the Bluebirds claimed a creditable 1-1 draw away to Middlesbrough. Photo: Stu Forster
7. Gustavo Hamer (Sheffield United)
The midfielder scored the Blades' opening goal during their 2-1 win away to Watford. Photo: Richard Pelham
8. Abu Kamara (Hull City)
The winger bagged twice as the Tigers came from 3-1 down to draw 3-3 with leaders Leeds. Photo: George Wood