After an edgy start, goals from Morgan Gibbs-White, Iliman Ndiaye and Sander Berge inside the opening 25 minutes put any nerves to bed and made it a day to remember in the sunshine.
Enda Stevens scored his first goal since February 2020 after the break to wrap up the win in front of a buoyant home crowd.
“We wanted to do it our way,” Blades boss Paul Heckingbottom said after the full-time whistle.
"We didn’t want to be thinking about results elsewhere.
“To do that, you’ve got to focus on your performance and do things right. The boys were good.
“I’ve said all along that we’ve got good players. We can’t win every game – we know we’ll not – but we’ve extended the season, which is great and what we all wanted.
“We couldn’t have done much more in terms of being aggressive, stopping Fulham, trying to play forward quick, creating chances and we scored the goals.
“We’ll celebrate being in the play-offs and we’ll enjoy it, however we haven’t won anything and haven’t achieved anything. We’ve got more to do.”
The result sets up a play-off semi-final tie against Nottingham Forest, with the first leg at Bramall Lane next Saturday.
Looking ahead to the clash, Heckingbottom added: “You’ve got one half here and one half away. We know each other well. They will be huge games.
"It’ll be a full house here and then roles reversed away at the City Ground.”
Fulham ‘not good enough’
For Fulham it was a game too far after a celebratory season, which ends with them as champions and 90 points, as well as 106 goals.
“It wasn’t the way we wanted to finish the season. It was a tough result for us,” boss Marco Silva said.
“We started well and dominated until they scored the first goal. The way we conceded the second and third goals reflects our performance.
“It is a good thing that in the last 15 days we had two moments to celebrate. The players deserve it.
“With the ball, we were really good in certain moments of the game but without the ball it was not good enough."