Barrow scored two goals in the last 11 minutes to beat 10-man Tamworth.
The hosts went ahead as Kyle Patterson nodded home Callum Wilson's cross, but Paul Smith's volley drew Barrow level.
Richard Tait was sent off for a poor tackle on Richie Baker and the 10 men went ahead thanks to a well-drilled finish from Patterson.
Wilson set up Cook to level for Barrow and the latter's second goal turned out to be the winner, as he slammed home from inside the six-yard box.
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