United's U18s slipped to defeat in Lancashire on Saturday, despite having chances throughout the game.
Conceding on the stroke of half-time gave the hosts the momentum and three further strikes after the break sealed with the win for the Trotters.
Bolton had the first opportunity after the Blades failed to clear a long punt forward, but Ramsdale was quickly off his line to make the save. At the other end Smith beat two defenders before crossing deep to the back post where Mallon headed narrowly over.
United were again grateful to Ramsdale on the half hour as he made a save from point blank range, prior to Gordon failing to connect with Mallon's delivery which went agonisingly across the face of goal.
With the first-half looking likely to end in stalemate, the home side opened the scoring with the last meaningful action of the opening 45 minutes.
Despite the disappointment of conceding before the break, United started the second-half positive with Mallon again a threat, this time teeing up Hallam who fired just wide.
But seven minutes into the second period, Bolton doubled their lead with a swift counter attack and on the hour made it three with another quick break.
Litchfield replaced Slew as United looked for a lifeline, with Smith having a shot saved after good work by Hallam.
The visitors were enjoying a decent spell of pressure, despite the earlier concession of two goals and Mallon had a shot cleared off the line before Gordon saw his attempted block of the clearance go just over the bar.
Smith, Mallon and Hallam all had further half-chances for the Blades, prior to Bolton adding a fourth goal in the latter stages.
Blades: Ramsdale, Charlesworth, Cummings, Semple, Brown, Smith (Ramsey 82), Gilmour (Maw 64), Gordon, Mallon, Hallam, Slew (Litchfield 61).