United were playing under new boss Micky Adams for the first time and he watched on in delight as Mark Yeates fired the visitors ahead in the ninth minute.
Winger Chris Eagles brought the Clarets level in the 29th minute and two goals on the stroke of half-time from Chris Iwelumo and Jay Rodriguez put the hosts 3-1 ahead at the break.
A penalty from the in-form Ched Evans shortly after the restart hauled the visitors back into contention but Burnley added a fourth late on to seal victory through substitute Steven Thompson.
Source: PA
Source: PA