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.
5. Jack Robinson 6.5
Was inches away from giving the Blades an early lead, but his angled drive went just the wrong side of Collins' post. Defensively solid and offered an attacking threat too Photo: Andrew Yates
6. Rhys Norrington-Davies 6
Was defensively solid in the first half and carried that into the second, shutting down a Barnsley counter-attack at 1-0 that saw them have a 3-on-1 advantage in their favour. Good dinked cross saw Gibbs-White's header saved by Collins Photo: Andrew Yates
7. Ollie Norwood 6
Showed good examples of both sides of his game early on, with a good tackle halting a promising Barnsley attack before spraying the ball wide to start one for United. Good awareness with the quick free-kick for Berge's goal Photo: Will Matthews
8. Sander Berge 7
Had a quiet first 45 minutes by his standards but got on the scoresheet in the second half, bundling home from close range from Hourihane's good cross. Replaced by McBurnie and United will pray he comes back from international duty fit and firing. Extra point for the goal Photo: Darren Staples