In a match often devoid of quality in the final third, Odsonne Edouard came up with the decisive goal early in the second half to secure a merited win for Roy Hodgson's troops.
There were debutants on both sides from the first whistle, as Jefferson Lerma slotted into the Palace midfield, while Benie Traore spearheaded the charge for the Blades.
Sheffield United were on the front foot early doors, and academy product William Osula tried to bend a curling strike into the far corner with 12 minutes gone, but Sam Johnstone breathed a sigh of relief as his effort flew just wide.
Hodgson's side soon began to take the game by the scruff of the neck, with Eberechi Eze unsurprisingly trying to conjure up a moment of magic, but the Blades defence was holding firm.
There was nothing much to write home about in the first half, but just four minutes into the second period, the Eagles opened their account for the 2023-24 season thanks to a classic centre-forward's goal from Edouard.
A burst of pace from Jordan Ayew on the right flank took him past Ben Osborn, and the Ghanaian's cross was on the money for Edouard, who stuck out his right foot to prod Palace into the lead from inside the six-yard area.
Paul Heckingbottom's men were made to pay for stagnant defending, but Osborn tried to make amends with a powerful drive in the 63rd minute, which was stopped en route to goal by a sliding Joachim Andersen.
Edouard had the ball in the back of the net again in the 70th minute, but the offside flag denied the Eagles their second, which they nearly bagged in the 72nd minute as Jeffrey Schlupp forced Wes Foderingham into a strong save.
However, Sheffield United were not giving up the ghost in an open second half and struck the side netting through Osula in the 76th minute, but the goal that the Blades craved was not forthcoming.
Once again, Foderingham kept the hosts in the game with a stunning save from an Andersen header in the 86th minute, but Heckingbottom's side ultimately got off to a losing start on their own patch.
Next up for the Blades is a trek to the City Ground to meet Nottingham Forest next Friday, while Palace have nine days to recover ahead of a home clash with London rivals Arsenal on August 21.