Marissa Thomas, BBC Sport
The Hatters' six-game unbeaten run came to the end as their usual fighting spirit was lacking in front of a home crowd at Kenilworth Road.
In the 20th minute of the match, Luton fans applauded in memory of fellow fan and steward Hassan Ali who passed away at the age of 20 after a battle with leukaemia.
Carlton Morris scored from the penalty spot to reduce the deficit but Luton did not do enough to get an equaliser before Vini Souza made it 3-1 to the Blades.
Despite their recent good form, Rob Edwards' side are just a point above the relegation zone in 17th position and they will now be looking nervously over their shoulders.
Luton host Man United next weekend and will look to get back to winning ways with the threat of relegation still looming large.