A Jason Walker penalty was enough to give Barrow their second away win of the season at Crawley.
Walker scored from the spot after he was brought down in the area by Karl Broadhurst who received a red card - his second in three games.
Earlier Barrow almost took the lead when Andy Bond had a shot parried by keeper Simon Rayner.
Eddie Hutchinson could have grabbed an equaliser for the home side but his close-range header went wide.
Crawley manager Steve Evans told BBC Sussex:
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"I don't think there's anyone in the ground, apart from the referee, who thinks it was a penalty.
"But that's not the reason why we got beaten. We got beaten because we didn't take our chances.
"Barrow worked hard, but if they say anything other than that we took them apart in spells, then they're in fairyland."
Crawley Town: Rayner, Rusk, Rents, Broadhurst, Quinn, Cogan, Hutchinson, Pinault (Wilson 76), Killeen (Smith 70), Louis, Willock (Ademeno 56). Subs Not Used: Forrest, Jordan.
Sent Off: Broadhurst (74).
Booked: Pinault.
Barrow: Tomlinson, Spender, Jones, Jelleyman, Pearson, Wainwright, Bond (Boyd 90), Sheridan, Rutherford, Walker, Shaw. Subs Not Used: Deasy, Logan, Dugdale, Cook.
Booked: Sheridan.
Goals: Walker 75 pen.
Att: 1,051.
Ref: R Martin (Weston-Super-Mare).
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