James Scowcroft helped Palace make it 12 games unbeaten as boss Neil Warnock won on his return to his former club.
Paddy Kenny denied Palace teenager Sean Scannell before Julian Speroni saved a Rob Hulse shot with his legs and then Jon Stead fired well wide when through.
Scowcroft netted on 38 minutes from Ben Watson's free-kick and Tom Soares went close to making it 2-0 after the break.
The Blades dominated after that but Speroni again thwarted Hulse, who also shot wide from two yards out.
Sheff Utd boss Bryan Robson:
"It's killing us missing the chances we're missing. The commitment and workrate was good but we didn't take our chances.
"I don't think it's anything to do with a lack of confidence - we just haven't been getting the breaks.
"If we continue to create the amount of chances we're creating, they'll start going in at some stage."
Crystal Palace boss Neil Warnock:
"I had a fantastic welcome and couldn't have asked for anything more. I felt quite emotional after the game and couldn't talk to the players.
"We are limited but the lads gave their all and that's all I can ask for. We're not the finished article but we've moulded a unit and worked hard and we're getting results.
"We will slip up but I think anyone can get into the play-offs this season."
Sheff Utd: Kenny, Bardsley, Kilgallon, Lucketti, Naysmith, Gillespie (Sharp 53), Tonge, Montgomery, Armstrong (Hendrie 63), Hulse, Stead.
Subs Not Used: Bromby, Bennett, Carney.
Booked: Hendrie.
Crystal Palace: Speroni, Butterfield, Lawrence, Hudson, Hill, Watson, Soares (Ifill 90), Derry, Scowcroft, Morrison (Fletcher 73), Scannell (Hills 78).
Subs Not Used: Freedman, Fonte.
Booked: Derry, Soares, Butterfield.
Goals: Scowcroft 38.
Att: 23,982
Ref: Andy D'Urso (Essex).
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