Ashley Ward scored the only goal of the match in the 26th minute to give Danny Wilson's side the three points.
The match also saw Jan Aage Fjortoft make his Oakwell début.
Barnsley Player subscribers can watch highlights from that match here.
Teams
Reds: Watson, Eaden, Markstedt, Morgan, Barnard, Tinkler, Sheridan, Redfearn, Marcelle, Fjortoft (Liddell 88), Ward.
Subs not used: Krizan, Bullock, Bosancic, Hendrie.
Subs not used: Krizan, Bullock, Bosancic, Hendrie.
Palace: Miller, Gordon, Hreidarsson, Linighan (Ginty 84), Edworthy, Smith, Fullarton, Roberts, Bent, Dyer, Brolin.
Subs not used: Nash, Boxall, Quinn, Thomson.
Subs not used: Nash, Boxall, Quinn, Thomson.
Attendance: 17,819.
Referee: M. D. Reed