United led 1–0 at half-time through a goal from Callum O'Dowda.
An own-goal by Chey Dunkley early in the second half was followed by goals from Ashley Fletcher and Adam Hammill to give Barnsley a two-goal cushion.
A header from Danny Hylton in the 76th minute reduced the deficit, but United were unable to find an equaliser in the remaining minutes and suffered defeat at Wembley for the first time in their history.
[1] Both Barnsley and Oxford United were promoted from their respective leagues at the end of the 2015–16 season.
Winners Barnsley were promoted to the Championship, after beating Millwall 3–1 in the League One play-off final at Wembley Stadium on 29 May 2016.