Tyler Smith netted a last-gasp winner, as United made it four wins on the spin.
Bolton looked set for a share of the spoils, having cancelled out Horatio Hirst's second-half opening, but the Blades struck late to put them on the brink of winning the league title.
The game burst into life just after the hour when HIRST volley United in front from Charlesworth's right-wing cross.
Bolton responded with an excellent long-range free-kick to restore parity ten minutes later, but at the death, the Blades snatched the victory.
Stewart and SMITH combined to create an opening and the latter unleashed an unstoppable effort into the top corner to send Shirecliffe into a sea of celebration.
Blades: Warhurst, Charlesworth, Brown, Cantrill, Cummings, Gilmour, Ford, Greaves (Stewart 77), Hallam, Hirst, T. Smith (Hawkes 90).
Unused: Parkhouse, Dewhurst, Potts.