After some outstanding goalkeeping from both Illan Meslier and Aaron Ramsdale, Patrick Bamford headed home a Jack Harrison cross in the 88th minute for the only goal of the game.
Graham Smyth, the YEP's chief football writer, hands out the scores.
1. Illan Meslier
9 - Two sublime saves aside he was solid, brave and distributed the ball well. Photo by MOLLY DARLINGTON/POOL/AFP via Getty Images.
2. Luke Ayling
7 - A lot of Blades pressure came down his side and he was largely solid. Wasn't as slick in the final third as he can be. Photo by Oli Scarff - Pool/Getty Images.
3. Liam Cooper
8 - Good on the ball, in the air and in the tackle. Ensured Leeds kept it sensible in the final minute. Photo by Oli Scarff - Pool/Getty Images.
4. Robin Koch
7 - Lots of sensible defending, won headers, stood up in challenges. Didn't always get the better of his men but a solid performance. Photo by Oli Scarff - Pool/Getty Images.
5. Kalvin Phillips
8 - Got on the ball to good effect, still brought physicality to the game even after being booked early. Covered a lot of ground. Photo by Molly Darlington - Pool/Getty Images.
6. Stuart Dallas
8 - A decent first half, a superb second half in midfield. Drove Leeds forward, won the ball, created danger. He was everywhere. Picture by James Hardisty.