Beaten at Leicester and Nottingham Forest in their previous two away matches, the Clarets twice fell behind to goals from Theo Robinson and Jamie Ward.
Chris Eagles equalised on each occasion - the second came on the rebound after his penalty was saved by Brad Jones following Ward's sending-off - before providing the cross for Wade Elliott to head Burnley in front.
Chris McCann, starting his first game of the season following reconstructive knee ligament surgery last summer, sealed the win midway through the second half as Eddie Howe's side moved level on points with six-placed Forest.
The result set up Burnley for Monday`s home clash with Portsmouth before they face rivals Leeds in a crunch showdown at Elland Road next Saturday.
Source: PA
Source: PA