Chris Basham, who played as a makeshift midfielder, scored the winner from 20 yards after Billy Sharp capitalised on a slip by Liam Cooper to play him in.
Tyler Roberts hit the post with a curling shot from 15 yards. The home side created some good chances but they failed to hit the target.
Kiko Casilla was shown a straight red card in injury time. Pontus Jansson, who ended the game in goal following the goalkeeper’s dismissal, poked wide from close range after Leeds had used up all three of their substitutes.
The Swedish defender was struggling with a knee injury during the game. However, Marcelo Bielsa refused to comment on it when asked about Jansson’s injury scare.
“I don’t know,” said Bielsa, as quoted by Leeds Live.
As a result of the win, Sheffield United have jumped over Leeds in the Championship table. Leeds have dropped to third in the table, three points behind league leaders Norwich City.