The Blades led first inside 25 seconds through Ben Brereton Diaz's opener and then James McAtee restored their advantage after Ebere Eze's equaliser. Eze then levelled again in a breathless first half before Michael Olise, who like Eze was a constant threat to United all evening, scored a second-half winner.
United suffered an injury blow when new goalkeeper Ivo Grbic went off in the second half after taking a whack to the head from Jean-Philippe Mateta, and he will now be assessed ahead of the weekend clash with Aston Villa after being withdrawn as a concussion substitute. Here's how we rated United's players at Selhurst Park...
1. Ivo Grbic 5
Made his Premier League debut but didn't cover himself in glory for Palace's opener as he tried to anticipate Olise's cross but was subsequently left stranded when Eze stuck out a foot and poked into the unguarded net. His debut was cut short early in the second half when he was clattered by Mateta and after treatment he made way, despite pleading with United's doctors to be allowed to continue
2. Jayden Bogle 5
Looking to put his nightmare against Brighton behind him and was better here, never afraid to try and make something happen down the right wing even if it didn't always come off. A great cross late on was begging to be converted and he did well to pick out Osula in the middle, but his shot was blocked before it could get to Henderson
3. Anel Ahmedhodzic 5
Had a real physical battle against the awkward Mateta and at the other end was almost the hero with a late equaliser as he got his head to sub Larouci's shot and diverted it goalwards, only to see it beat Henderson but rebound off the crossbar and to safety
4. Jack Robinson 5
He and Ahmedhodzic didn't help their goalkeeper out when allowing Eze to run unchallenged and meet Olise's cross for the first Palace goal. Was booked in the first half for upending Eze and was replaced with eight minutes of normal time to go by Larouci