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.
At the other end of the table two goals from Mustapha Bundu helped relegation-threatened Plymouth stun play-off hopefuls Coventry 3-1 to claim their third home win in a row.
Cardiff, meanwhile, suffered a huge blow to their survival hopes as a free-kick screamer from Cameron Brannagan salvaged a 1-1 draw for Oxford and soured Aaron Ramsey's first game as interim Bluebirds boss.
The remainder of the teams in acute relegation danger all won, Derby earning a much-needed 3-1 victory over West Brom with goals from Ebou Adams, Jerry Yates and Nathaniel Mendez-Laing.
That was followed by Albion announcing the departure of manager Tony Mowbray with their play-offs hopes effectively extinguished.
Hull came from behind to beat fellow strugglers Preston 2-1 with two Joe Gelhardt penalties while a terrific second-half display saw Luton give their hopes a boost by beating play-off chasing Bristol City 3-1. Thelo Aasgaard, Carlton Morris and Isaiah Jones scored Town's goals.
Colby Bishop's goal earned Portsmouth a 1-0 win over 10-man Watford to seal their safety, Kusini Yengi making a substitute appearance.
Tyrhys Dolan kept alive Blackburn's 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 Mihailo Ivanovic scored twice to sink Norwich 3-1 at The Den.
Middlesbrough's ambitions were dented by a damaging 2-1 loss at Sheffield Wednesday after substitute Anthony Musaba scrambled home an 89th-minute winner.
