Louie Sibley gave the Rams the lead just before the break but the visitors couldn't see the lead out with a strong United second half being the difference.
The emergence of talent
The game started with 11 players aged 21 or under with both managers sticking to their pledge of giving youth a chance in this competition.
Some of these are established names such as Jayden Bogle and Sibley whilst others are using the opportunity to make a name for themselves. One of those was Blades defender Kyron Gordon, who grabbed the assist for Freeman's finish.
Gordon made his professional debut for the side against Carlisle in the first round of this tournament.
Jack Stretton of Derby also impressed and has featured in the squad of late. The striker was the most accurate passer on the pitch of anyone who played 45 minutes or more (100%). In the Championship this season he has started three times and scored once.
Rooney told RamsTV that despite the loss he was happy with the young players and their performance: “We are out of the cup, but there is so much more that we have gained from this game.
“The same can be said of the Round One tie against Salford City too, but also I thought we were better in this one than we were against them.
“We came here and dominated. The first half was excellent and in the second half I still felt we were the better team.
“I thought the reaction to conceding the first goal was very good. Obviously a mistake has cost us the second goal, but I can stand here and say I am proud of the players for the performance they put in.”
Finally, young striker Daniel Jebbison was given another chance but was bought off after 45 minutes, leaving fans to speculate about his future. Boss Slavisa Jokanovic told the Yorkshire Post: "We will see. To be honest, Jebbo can be our future. For another side, I am not thinking about selling him or something like this.
"I repeat, he can have a really good future for Sheffield United.
"I want four or five players, that's it. We urgently need new faces and fresh blood and a little bit more confidence to be competitive."
The 19-year old put in a man of the match performance despite his team's defeat. The attacking midfielder had five shots, two on target, two off target and one blocked.
He won seven of his 11 duels and had a pass accuracy of 64%. He completed 100% of his attempted dribbles and was fouled three times by his opposition.
At such a young age Sibley offers a sense of experience and reliability that Wayne Rooney needs in his Derby side.
It's been a tough season for everyone in Derby so far but this performance should give Sibley confidence going forward that he needs to put in a strong contribution this season.
A confidence boost for Sheffield United
The Blades currently sit in the relegation zone in the league having won none of their four matches. However, a second win in the cup, this time against a Championship side should give them hope going forward.
Unfortunately this year there are no easy games in the Championship but for newly relegated Premier League side there should be some teams easier to beat then others. Hull City, Peterborough United and Luton Town are all sides, at the start of the season, United would have been tipped to beat and now off the back of this win they may feel more inclined to do just that.