New signings Mounir El Haimour, Iain Hume and Hugo Colace all played a part in the game.
Jon Macken fired the Reds in front after 23 minutes and Buxton equalised through a stunning goal by Gavin Knight on 40 minutes.
Ryan Kidd made seven half time subs and within a minute of the restart, the Reds were back in front through sub Jamil Adam, when he turned Jacob Butterfield's free-kick in.
Adam made it 3 on 68 when he pounced on a save from an El Haimour shot. Then Macken bagged his second and Barnsley's fourth on 78 minutes after good work from Mounir El Haimour.
Reds Team: Steele, Hassell (van Homoet 45), Foster, Souza (Atkinson 45), Kozluk (Potter 45), Leon (Togwell 45), Colace, Howard (Johnson 45), El Haimour, Hume (Adam 45), Macken.