Goals from Chris Wood and Souleymane Doukara were enough to see off a Rotherham United side who remain 11 points adrift of safety despite a spirited showing despite playing for more than an hour with ten men..
It was a wretched day for the Millers, who lost Greg Halford and goalkeeper Lee Camp to injuries during a first half that also saw Peter Odeminwgie rightly shown a straight red card.
Odeminwgie was dismissed for a disgraceful elbow on Liam Cooper that left the Leeds defender requiring extensive treatment.
By then, the visitors led thanks Wood firing in from close range after Charlie Taylor had capitalised on woeful defensive play from Stephen Kelly.
Doukara added a second in seven minutes of stoppage time at the end of the first half, poking a low shot beyond Lewis Price following good work from Kemar Roofe.
Leeds were then guilty of being far too casual and this gave Rotherham hope. Richard Wood pulled a goal back four minutes from time with a bullet header that set up a frantic finale.
An almighty goalmouth scramble then ended with Dominic Ball being presented with a chance just two yards from goal only to blaze high and wide.
Kalvin Phillips then had to head clear following excellent work by Izzy Brown in the fourth minute of stoppage time that led two defenders trailing.
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