Jake Cooper's header in the 94th minute ensured that Neil Harris' side left South Yorkshire with a point, cancelling out Gary Madine's opener early into the second-half.
The visitors were piling on the pressure late into the contest and thought they would have found the net when Tom Elliott's header beat goalkeeper Dean Henderson.
However, defender John Egan was backtracking and with the ball going over his head, the Blades man stuck out an arm and deflected the ball away by using his hand.
United were desperate for the three points and, even though Egan was shown a straight red card, Ben Marshall smashed his penalty onto the crossbar and they would have thought that was the chance gone.
Unfortunately for him though, Cooper was there in the dying seconds to deny Sheffield United victory. Leeds would then beat Sheffield Wednesday in the late kick-off to move three points clear in second.
Discussing the result, Blades boss Chris Wilder said: "When they go a goal down they have to show more ambition, but we just went backwards instead of trusting the shape. We went backwards in thought and in play and paid the price.
"After the goal they deserved a point, but we never showed enough ambition to go on and score the second, which is uncharacteristic from our team.
"They missed a penalty, but we didn't just deserve a point. We have deserved more in other games like today, but that is how football is.
"We played safe and didn't go for the jugular. We played backwards and square and sat in, so I'm not surprised they got back into the game and deservedly so.
"They had a drive to get back into the game and that's one of their characteristics. It's stinging that we didn't get those extra two points."
