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.
1. Illan Meslier
7 - Didn't have too many saves to make but dealt with everything that came his way. Brave at set-pieces, again. Picture by Mike Egerton/PA Wire.
2. Luke Ayling
6 - The central defensive role stopped him from making the same impact on the game. Looked unsettled by the chopping and changing. Effort there, as always. Photo by George Wood/Getty Images.
3. Liam Cooper
8 - Made big tackles, blocks and headers. Denied Barnsley at key times. A leader's performance.
4. Gaetano Berardi
6 - Looked lost at times as he was sent back and forth between positions. Seemed to pick up a niggle but stayed in the fight.