The home side also spurned a great opportunity when Neil Danns was brilliantly put through by Nicky Carle, but could only rifle his shot wide of Kenny's left-hand upright from inside the area.
Apart those two chances, Neil Warnock's men spent most of the afternoon chasing their opponents around the Selhurst Park pitch.
Although Ward and Halford went closest for United they also created other good openings with David Cotterill smashing over from six yards and Darius Henderson failing to get on the end of a superb left-wing cross by fractions.
But for all of the possession and chances they created the Blades could not find a past Palace's last line of defence - something they would have rued had the game between Reading and Birmingham finished in a draw.
United will now play Preston in their Championship semi-final playoff tie, with the first leg at Deepdale.
Crystal Palace boss Neil Warnock:
"While I'm tinged with being a Blade it was solely a manager's job I had to do, but it wasn't easy for me.
"I shook Kevin Blackwell's hand before the game and told him I wanted to win. We couldn't do that, but we competed really well and had some good chances.
"I couldn't have asked for anything more from my players. I can go back to being a Blade now and support them in the play-offs.
"I think once they get over the results this weekend, they will be the favourites to go up."
Sheffield United manager Kevin Blackwell:
"It was a massive pressure game and they didn't buckle, they just kept going.
"I can't complain about the display at all and now we just need to reproduce that in the play-offs.
"You need breaks in these games and we just didn't get them - Speroni made save after save.
"We needed something to go our way and it just didn't happen for us. If I could take anything away from Crystal Palace it would be Lady Luck. I'd put her in the boot of the car and hope that she can rear her head in the play-offs when you need it."
Crystal Palace: Speroni, Lawrence, McCarthy, Jose Fonte, Hill, Ertl, Danns (Scowcroft 90), Carle, Moses (Rui Fonte 55), Kuqi, Stokes (Hills 72). Subs Not Used: Clyne, Cadogan.
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