Barnsley had taken the lead on their academy pitch at Oakwell with Rhys Oates, who set up Kane Hemmings' goal in the 5-1 loss at Crawley, scoring from the spot after he was clumsily brought down by Sam Berry in the opening five minutes.
United, managed by former Barnsley player Chris Morgan, responded well and were level on 12 minutes when Dominic Calvert-Lewin was on hand to tap home a cross from CJ Hamilton.
The visitors ensured they went in at the break ahead when Calvert-Lewin won a penalty after being bundled over by December signing George Williams.
Callum McFadzean sent Adam Davies in the Barnsley goal the wrong way.
Barnsley had a couple of chances to get level in the second half with George Maris cleverly flicking a Sean Goodwin cross goalwards.
Winger Dale Jennings also had a couple of shots on goal before he was replaced by Sam Hanna.
Out of favour central midfielder James Bailey completed more than 70 minutes in the game before being taken off for Pedro Carneiro.
United arguably had the better of the second period with Calvert-Lewin and Ben Whiteman trying their luck while Wath teenager and Welsh youth international Ioan Evans looked solid in the heart of their defence.
Barnsley: Davies, Williams, Jeffs, Gooda, Templeton, Maris, Goodwin, Bailey (Pedro 67), Jennings (Hanna 72), Oates, Kassouri (J Brown 77). Unused: Walton, Reilly.
United: Willis, Paling, McFadzean, Dimaio, Berry, Evans, Coustrain, Whiteman, Calvert-Lewin, Wallace, Hamilton.