But the win potentially came at a cost when skipper Billy Sharp limped off in the second half, adding another headache for boss Paul Heckingbottom in a season of injury struggle so far.
United were far from at their best in the first half against Barnsley, who could have gone ahead early on when Matty Wolfe saw an effort well saved by Wes Foderingham.
But the home side went ahead perhaps against the run of play when Sander Berge converted from close range, and Morgan Gibbs-White put the gloss on victory after going around Brad Collins and slotting home after good play from substitute Oli McBurnie.
9. Conor Hourihane 6
Facing his former club after replacing Iliman Ndiaye, Hourihane had an indifferent first half but found a moment of quality with a superb cross for Berge to bundle home Photo: Will Matthews
10. Morgan Gibbs-White 8
Was quiet by his own high standards in the first half but showed a customary touch of quality by going round Collins and putting the Blades 2-0 up. Makes things look so easy when he's on form, and works so hard for the cause as well Photo: Andrew Yates
11. Billy Sharp 6
Gave United another big injury scare when he went down, and stayed down, in the second half. After some treatment he was replaced by Jebbison and United will be desperate for that to not be serious after their injury problems this season Photo: Darren Staples
12. Subs: Daniel Jebbison 6
Came on for Sharp and had a decent chance but he put it over the top Photo: Darren Staples