Barnsley scored twice in dominant second period that saw wholesale changes in both lineups, with Andy Hammill converting a spot kick after a handball.
Despite their dominance, Celtic held firm until six minutes from time when Hammill turned provider, and Jack Cowgill headed home.
McMillan, Wylie, Astley, Hughes, Ryan, Platt, Osei, Wright, Farrell, Craig, Mukendi. Subs: Lynch, Gray, Owens, Matthews, Freeland
Townsend, Bree, Roberts, Mawson, White, Henry, Moncur, Scowen, Lee, Winnall, Watkins. Subs: Townsend, Yiadom, Cowgill, Nyatanga, Evans, Tuton, Harris, Hourihane, Hammill, Payne, Jackson.