Second-half strikes from Jordan Slew and Richard Cresswell did the damage as the Blades made it back-to-back wins in League One.
United had the best chance of the opening exchanges but Slew fired wastefully wide when free on the left.
Gary Alexander then nodded Myles Weston’s curling cross narrowly over the bar before the Blades burst into life after the break and went ahead four minutes after the restart through Slew.
Cresswell found time and space in the visitors box to tee up the 18-year-old, who fired home a deflected drive from close range.
And United were again celebrating on 70 minutes as Cresswell tapped home Matthew Lowton’s low cross to seal the win.