Tony McMahon, who scored from two free-kicks in the recent league win at Crawley, gave United the lead on 17 minutes.
His goal again came direct from a free-kick, this one from 20 yards out and in the centre of the goal.
Midway through the second half, Dave Kitson continued his own good goalscoring form by doubling the Blades’ lead.
Nick Blackman put the result beyond doubt with a third in the 87th minute to end the resistance of the League Two side.
United lost Matt Hill to injury after a clash of heads.
Blades boss Wilson said: “He was very groggy after a clash of heads. We’ll pick him up from hospital on the way back.
“Matty was feeling it. We’ll know more later. It’s too early to say.”