The Leeds players, who had earlier done their bit by beating Stoke City 6-0, watched on from the Billy Bremner suite at Elland Road as John Brownhill scored twice for Burnley either side of Tom Cannon's first goal for the Blades.
Joel Piroe had struck four goals for a rampant Leeds side, Junior Firpo and Willy Gnonto also scoring.
"It's amazing. If you look at the scenes here, as it was after the final whistle, just pure excitement," Leeds captain Ethan Ampadu said.
"Within ourselves we've got another target, so we can enjoy this now, but we've got another target we want to achieve. But right now, it's very good."
Leeds boss Daniel Farke, who won promotion from the Championship to the EPL twice with Norwich City in 2019 and 2021, said he was "lost for words".
"You can see the atmosphere here, it's incredible. It's well deserved, 94 points at this stage is unbelievable. The lads should celebrate, all our supporters should celebrate.
"We will make sure that this Easter Monday will last for one or two more days.
"We played fantastic last season, with 90 minutes, before the heart-breaking game at Wembley, but to show resilience and keep going, we deserve today to celebrate."
At the other end of the table, relegation-threatened Plymouth Argyle stunned play-off hopefuls Coventry City 3-1 to claim their third home win in a row.
Cardiff City suffered a huge blow to their survival hopes as a stunning Cameron Brannagan free kick salvaged a 1-1 draw for Oxford United.
The remainder of the teams in acute relegation danger all won, Derby County earning a much-needed 3-1 victory over West Bromwich Albion.
Hull City came from behind to beat fellow strugglers Preston North End 2-1, while a terrific second-half display saw Luton Town give their hopes a boost by beating play-off chasing Bristol City 3-1.
Colby Bishop's goal earned Portsmouth a 1-0 win over 10-man Watford to seal their safety, with Socceroo Kusini Yengi making a substitute appearance.
Tyrhys Dolan kept alive Blackburn Rovers' chances of making the play-offs after a hard-earned 1-0 win at Sunderland.
Millwall are just three points off sixth-placed Coventry in the play-off places with two matches to go after a 3-1 win over Norwich at The Den, but Middlesbrough's ambitions were dented by a damaging 2-1 loss at Sheffield Wednesday.
