Efforts from Sheffield United were frequent before the hour-mark. Brooks and Jili Buyabu tried their luck, though neither of their efforts were troubling Goodman in the Palace goal. The hosts were effectively camped in the Palace half as they looked to find an equaliser.
With 15 minutes remaining, Sheffield United managed to equalise. Owen Hampson, who scored for the Blades in their 1-2 defeat to Palace Under-18s, danced into the box and managed to get a side-footed shot away to level.
The Eagles were not disheartened after conceding, in fact they went straight down the other end and instantly responded. Gordon picked up the ball on the byline and drove into the box before firing in a fierce shot from the narrowest of angles that beat Amissah at his near post.
After going behind again, the hosts threw everything at it in search of another equaliser. Palace were firmly camped deep in their defensive third, set up to absorb the pressure.
Nickeson Gomis and Antoine Hackford were denied late on by two fantastic Goodman saves, while Hampson hit the post in the fourth minute of stoppage time for the hosts.
The 10-men of Palace held on through six minutes of time added on, seeing off the remnants of the Sheffield United attacks. The result sees Palace get off to a winning start in Group E, though they are second to Bristol City on goal difference.
Sheffield United: Amissah, Sachdev, Buyabu, Potter, Barrett (Gaxha, 65), Gomis, Hamrson, Maguire, Williams (Hackford, 59), Marsh, Brooks.
Subs not used: Williams, Wharton, Pitan.
Crystal Palace: Goodman, Rodney, Balmer, Grehan, Adaramola, Ozoh, Wells-Morrison, Phillips, Omilabu (Akinwale, 65), Ola-Adebomi (Imray, 45), Gordon.
Subs not used: Raymond, Mooney, Cadgoan.