Ian Ross scored a debut goal to settle a dour clash with Boston.
The Blades' homegrown star capitalised on Keith Gillespie's corner to spare the Championship side's blushes.
Chris Armstrong should then have doubled the advantage but was wasteful when presented with a great chance to shoot inside the box.
And then Paul Ifill was unlucky not to score, but flowing football was in short supply and the Blades will simply be relieved to be through.
Sheff Utd: Barnes, Kozluk (Wright 62), Morgan, Bromby, Geary, Gillespie (Forte 86), Alan Quinn, Ifill, Armstrong, Shaw (Mulligan 77), Ross.
Subs Not Used: Nix, Stephen Quinn.
Goals: Ross 50.
Boston Utd: Abbey, Canoville, Ellender, White, McCann (Whelan 84), Thomas, Rusk (Maylett 77), Talbot, Noble (Holland 77), Lee, Joachim.
Subs Not Used: Clare, Wright.
Booked: Ellender, Noble.
Ref: K Stroud (Dorset).