The 19-year-old England Under-20 international finished clinically from 20 yards after Alan Quinn had stepped over Keith Gillespie's corner.
The Blades, playing without eight of the side that beat Preston at the weekend, dominated in the opening minutes but could find no way past a stubborn Boston rearguard.
Transfer-listed Paul Shaw was inches away from connecting with a Gillespie cross and stand-in striker Paul Ifill almost found a way through after Alan Quinn neatly threaded the ball into his path.
The Pilgrims, hammered 3-0 by Cheltenham on Saturday, almost found a way through in the 25th minute as ex-Aston Villa striker Julian Joachim charged towards goal but was stopped in his tracks by a well-timed tackle from Chris Morgan.
Ifill showed his pace two minutes later weaving past three defenders before slamming in a fierce right-foot strike on the run that was palmed spectacularly past the woodwork by Nathan Abbey.
The Boston keeper pulled off a carbon copy save ten minutes later, as Republic of Ireland international Alan Quinn tried his luck from long range.
Midfielder Danny Thomas caught the hosts on the break minutes later with a strike that was hammered wide of the far post after his earlier shot had been blocked.
But Steve Evans' side were caught four minutes before the interval, full-back Rob Kozluk charging in to meet Derek Geary's precise cross but the angle was too tight and the ball flashed across the face of the goal.
Ross struck the killer blow before Abbey foiled Ifill with another eye-catching stop but could only push the ball into Shaw's path and from ten yards he headed over the target.