Davies broke the deadlock three minutes before the interval with a header and Holt made sure of the points for Nigel Clough’s side with the second in the 71st minute.
Holt had the first effort of the match with a header which was saved by Barnsley’s on-loan goalkeeper Joe Wildsmith.
Barnsley responded with a Conor Hourihane free-kick which struck the defensive wall and then a long-range drive from Josh Scowen which went narrowly wide.
The visitors dominated for the rest of the half with Jamie Murphy having an effort saved and Davies heading just over.
Blades defender Chris Basham had a shot deflected wide and a close-range effort from Ryan Flynn was blocked.
Davies then put United ahead, meeting Kieron Freeman’s free-kick with a superb looping header which went into the far corner of the net.
Barnsley had a couple of half-chances with teenage defender Mason Holgate heading wide and Hourihane’s effort was deflected off-target.
Holt added a second goal with a sweetly-struck drive from just outside the penalty area after the Barnsley defence had failed to clear.