A Lewis Richardson double extended the Clarets’ unbeaten start as they came from behind to go to the top of the Professional Development League.
That lead may be short-lived, with current northern group pace-setters Nottingham Forest playing Wigan Athletic on Monday night.
But Burnley did everything they could by stretching their undefeated start to 10 league games thanks to a superb second half performance.
Richardson struck twice in the space of 12 minutes to take his total for the season to four and three in the past two games.
And with the Clarets then digging in to rebuff a late counter-thrust from the Tykes, they put the ball in Forest’s court ahead of their home fixture against the Latics.