The Clarets were behind after just 15 minutes, and a further two goals in the final 10 killed off the game.
The positives of the day were the returns to long term absentees Nathan Lowe and Dan Agyei (pictured, above).
It was a rusty starts from Michael Jolley's side, whose squad was heavily depleted by eight recent loan moves.
Burnley named two trialists in the game with an untested line-up, but almost took an early lead, when winger Brad Jackson struck the right hand post early on.
However, the hosts soon took the lead. Clarets keeper Dan Nizic, fresh from being on the bench for the first team at Brentford, wonderfully tipped over a curling effort from 20-yards to give United a corner.
The resulting set-piece was chipped to the near post, where a simple free header put the Blades ahead.
The Clarets struck the woodwork once more midway through the first half.
An outswinging corner from a trialist fell nicely to Aiden O'Neill 20-yards out, but the new professional was inches away from the leveller.
It was a much better performance from Burnley in the second half, and the scoreline could have been different, but for a penalty appeal waved away.
Tricky feet from Burnley's trialist forced a lunging challenge on the striker, but the referee quashed vociferous appeals.
Fresh from making his first appearance in eight months last week, Christian Hill then forced a superb save out of United's stopper.
The interim full back drove forward, before rifling an effort from 25-yards which was tipped wide at full stretch.
Lowe and Agyei made their appearances 25 minutes from time, and the duo almost made an instant impact.
Midfielder Lowe combined with the forward, before neat vision from Agyei played in the trialist, whose long range effort was clawed to safety.
And the former Wimbledon striker then came close 10 minutes from time.
This time a cross from the left found Agyei, who struck on the swivel, but a vital block on the line denied the equaliser.
The hosts then countered, where a chipped ball to the far post was coolly volleyed home.
And as Burnley went searching for a route back into the game, the Blades made it three with a pacey counter.
Burnley: Nizic; Birch (Lowe), Trialist, Norvock, Hill (Agyei); Frost, O'Neill, Wilson, Jackson; Dolling (Smith), Trialist