The contest was settled in the 28th minute by Michael Sollbauer's own goal but Barnsley missed a host of chances, especially in a dominant second half.
The YEP's chief football writer Graham Smyth hands out the scores following a game which has left Leeds on the brink of automatic promotion.
13. Gjanni Alioski (sub)
7 - Stretched Barnsley on the counter attack, put a couple of good balls into the area, one of which deserved a goal.
14. Pascal Struijk (sub)
7 - One bad pass aside played very well. Some good passes, won headers, by no means overawed by the occasion.
15. Jamie Shackleton (sub)
NA - Came on to add energy, pace and run in behind in the final minutes. Did that.
16. Jarred Gillett (referee)
7 - Missed one or two, including a trip on Bamford and one on Mowatt, but got the majority right and kept the game calm. Photo by Hagen Hopkins/Getty Images.