Blades boss Nigel Adkins made several changes, including the return of goalkeeper George Long and striker Billy Sharp dropping to the bench.
And the young Blades goalkeeper was called into action early on when he was forced to tip over Ashley Vincent's long-range effort.
The non-league visitors certainly were not shy in coming forward, former Sheffield Wednesday striker Deon Burton leading the line well.
The Blades had Conor Sammon and Che Adams up front, and were struggling to break Worcester down.
But the first goal of the contest came to the hosts. Sam Minihan was guilty of bringing down Che Adams and Jose Baxter converted from the penalty spot for his fifth goal of the season.
Stefan Scougall set-up a great chance for Baxter's second, but the midfielder could not keep his effort on target with the goal at his mercy.
It meant this tie was not over, and Worcester looked dangerous on the counter-attack.
Bob Harris saw his free-kick hit the crossbar, before bouncing down, hitting goalkeeper Nathan Vaughan, and roll away to safety,
Paul Coutts was next to be denied by Vaughan, as United pushed forward looking for a second goal.
That finally arrived, when superb work from Jamal Campbell-Ryce down the right saw the winger pick out Sammon, who flicked the ball over an exposed Vaughan.
And Kieron Freeman rubbed salt into the visitors' wounds, when he tapped home a late third goal.
For the latest from the match check out The Yorkshire Post’s live blog at...