Manager Chris Wilder admits his side are far from the finished article after they registered their third home win in three Championship games by beating Derby County at Bramall Lane.
United ran out winners courtesy of a brace from captain Billy Sharp and a Johnny Russell own goal, with Craig Bryson's late header just a consolation for the Rams.
And Wilder said: "You want to marry a good performance with a decent result, and I believe we've had both today.
"This was our biggest test at home this season, against quality opposition and a quality manager, and I'm delighted that we've played well and won.
"We're a learning club, our players are adapting to the division but I think we've made a decent start.
"We aren't getting ahead of ourselves, it's one game, but this is a great result for us.
"We can say that we aren't here just to make the numbers up or be the whipping boys, and any team that plays us, especially here, is going to have to do a lot of things very, very well to get a result against us."
The Blades took the lead when Scott Carson's attempted pass went straight to Sharp, who struck low into the bottom corner after four minutes.
Derby looked dangerous on the break, and Jack O'Connell was shown a yellow card for bringing down the onrushing Andreas Weimann before John Fleck's superb last-ditch tackle denied Matej Vydra, who looked odds-on to score.
Then Russell scored a calamitous own goal, turning in a cross to double United's advantage. Both sides missed good chances in the second half, before a stoppage-time header from Bryson set up a dramatic finish.
However, Sharp tapped into an empty net following a break after Carson had pushed forward to secure the three points for United.