It was a bitty start to the match at Oakwell, with Paul Coutts's header for the away side the only opening of the first quarter of an hour.
The hosts were struggling to break down the Blades and being restricted to efforts from distance. Josh Scowen took aim from range and saw his fizzing strike fly just wide.
United hit the woodwork in the 25th minute when a Holt header was left by Barnsley keeper Joe Wildsmith and bounced off the top of the crossbar.
Holt again went close 10 minutes later before the Blades' pressure told shortly before half time when Davies looped a header into the net from Kieron Freeman's cross.
Mason Holgate could have pulled Barnsley level in added time at the end of the first half, but was only able to head a close-range opportunity wide.
The Tykes started the second half well enough, but they couldn't break the visitors down. Their task of getting something out of the game was made doubly difficult 20 minutes from time when Holt stroked home from the middle of the box.
That was to be the final goal of the game as the Blades saw out the victory with relative ease.
Barnsley miss out on the chance to move within one point of the playoffs, while United get back to winning ways and move seven points clear of seventh-placed Bradford City.