Yorkshireman Rob Harker struck twice and Adam Phillips claimed his first goal as a Claret as the U23s re-ignited their push towards the top of the table.
Steve Stone’s youngsters remain the only unbeaten side in the northern group of the Professional Development League.
And a third win in four games lifted them up to third place as they over-powered the Blades at Bramall Lane.
Harker claimed his first goals of the season and could have left with the match-ball as he proved too hot to handle in the Steel city.
And a magnificent strike from midfield man Phillips proved another highlight on an afternoon the impressive Clarets again suggested they have what it takes to stay the pace in the race for the top.
Burnley made an excellent start and were set on their way when Harker opened his account just five minutes in.
The striker cut a frustrated figure a week ago when the Clarets let two points slip against Nottingham Forest.
But his training-ground work paid off when he powered a header into the top corner from a typically tempting Anthony Glennon cross.
The quality of balls into the box was a feature of the Clarets’ early dominance.
And when they mixed it up to find another route to goal that also paid off as Phillips doubled the lead with a sensational strike after a quarter of an hour.
This time, Ali Koiki fed the ball inside and from 30 yards Phillips hit a first-time drive into the top corner to give United’s former Dutch youth international Michael Verrips no chance in the Blades’ goal.
The home side included a couple of players with first-team experience – notably right wing-back Kieron Freeman – and former Manchester United and West Ham prospect Ravel Morrison.
But their response carried no cutting edge as the Clarets weathered a spell of pressure and had further chances themselves as Harker looked to get onto deliveries from Glennon and Ne-Jai Tucker.
The Blades did have opportunities to get back into the game just after the break but former Manchester United youngster Callum Gribbin dragged a shot wide after replacing a muted Morrison and Keenan Ferguson lifted an effort over the top.
And the Clarets made them pay when they opened up further daylight with a third goal 20 minutes into the second half.
The lively Koiki was denied by Verrips from a Tunde Bayode cross but from the corner that followed, Harker again stood tall to nod in Glennon’s delivery.
A Bayode slip at the other end let in Harry Boyes for an effort which Lukas Jensen did well to block before the Clarets’ winger made amends with a fine cross Lewis Richardson couldn’t convert.
And even though Jensen was called into action again to beat away a free-kick from George Broadbent – substitute Iliman Ndiaye heading the rebound over the top – the big Dane made sure he would secure a first clean sheet to keep the Clarets climbing.
Sheffield United: Verrips; Ferguson, Belehouan, Bryan; Freeman, York, Broadbent, Mallon (Boyes 31); Young (Ndiaye 79), Ompreon, Morrison (Gribbin HT). Substitutes: Amissah, Gordon.
Burnley: Jensen; Cooney, Younger, Wilson, Glennon; Tucker (Bayode 54), Phillips, N’Guessan, Koiki; Harker, Richardson (McGlynn 78). Substitutes: McMahon, Cropper, Benson.
Referee: Sam Mulhall