Looking to put the disappointment of their defeat to Leeds last weekend behind them, they could have taken the lead early on with McKenzie going close.
With 15 minutes gone however, Ronan Darcy produced a superb pass, playing in Eddie Brown who opened the scoring.
Brown then doubled his tally five minutes later with some excellent individual skill, although the Blades did halve the deficit from the penalty spot with the Bolton keeper unfortunate not to save their effort from 12 yards.
In the second half however, Laurence Smith hit an unstoppable shot from distance to restore Bolton’s two-goal advantage.
And with ten minutes remaining, Matty Barnes broke at the United defence before playing in Brown to complete his hat-trick and put the gloss on a fantastic result for Nicky Spooner’s youngsters.
Bolton: Alexander, Whalley, Edmundson, Riley, Senior, Preston, Darcy, Connell, Barnes, Brown, McKenzie
Subs: Boon, James, Smith, King-Harmes, White