The Tykes faced the League Two club in the FA Cup and were forced into extra-time.
Mads Andersen and Jordan Williams handed the hosts a healthy lead, however Barrow made it 2-2 with only 12 minutes left.
Before the full-time whistle was blown, both sides had another two goals apiece.
However, it was Poyas Asbaghi’s side that came up on top with an extra-time winner by Carlton Morris.
Barnsley will now travel to Huddersfield in the fourth round at the start of February.
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Before the full-time whistle was blown, both sides had another two goals apiece.