United's U18s saw their winning run come to an end in Lancashire on Saturday.
The Clarets scored the only goal of the game in the first-half to settle what was a tight affair throughout.
Burnley started the brighter of the two sides but failed to carve out any clear cut chances with sturdy defensive work from Cutts and Ferguson keeping the home side at bay.
After 25 minutes the Blades managed to create the best opportunity of the game, as Lawrence broke through but his shot was just shy of the post as the game remained even.
But in the 34th minute, Burnley scored what proved to be a decisive goal, netting direct from a free-kick that flew over everyone including goalkeeper Warhurst.
The second-half saw very few chances but the Blades would apply pressure throughout in an attempt to restore parity.
With 18 minutes left to go United came close to an equaliser as Cantrill's effort hit the post and Greaves had a follow up effort cleared off of the line in the final noteworthy action of the match.
Blades: Warhurst, Portman, Capello, Neal (Greaves 45), Cutts, Ferguson (Cantrill 45), Broadbent, Belehouan, Lawrence, Kelly (Weaver 65), Potts.
Unused: Capman, Ompreon.