Nick Chadwick bagged his seventh goal in 15 league starts for the Bluebirds
Barrow scored three times in the final half hour to earn a victory which propels the Bluebirds a big step nearer Blue Square Premier safety.
Crawley looked set for a point when Ben Smith headed home just before the hour to atone for his first-half own goal.
But Simon Wiles fired low into the bottom left corner three minutes later to put Barrow back in front.
Then, after Nick Chadwick struck from close range, Jason Walker wrapped it up with a shot from the edge of the box.
FA Trophy finalists Barrow, who still have a game in hand on most of the teams around them, are now six points clear of trouble.
The Bluebirds had a stroke of luck when they went in front not long before the break, Smith putting through his own goal after Walker's shot had come back off the post.
But, after Smith had redeemed himself by heading home Danny Forrest's cross from six yards, parity lasted for just four minutes before Wiles fired Barrow back in front from the edge of the area.
Wiles was then involved again in the 79th minute when his corner was met by Chadwick, who slotted home a right-foot shot from six yards. And the result was sealed three minutes from time by Walker.
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