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:
9. Andre Brooks (Sheffield United)
The wide man scored Sheffield United's winning goal during their 2-1 win against Watford. Photo: Justin Setterfield
10. Joel Piroe (Leeds United)
The striker scored Leeds' final goal during their 3-3 draw away to Hull City. Photo: George Wood
11. Zian Flemming (Burnley)
The Dutchman headed home the winning goal as Burnley claimed the derby spoils with a 1-0 win against Blackburn. Photo: Alex Livesey
12. MANAGER OF THE DAY: Scott Parker (Burnley)
The Clarets boss has also been recognised for masterminding Burnley's derby win at Ewood Park. Photo: Alex Livesey