A 76th-minute goal from substitute Nick Chadwick completed a comeback win for Barrow, who climb out of the drop zone.
Wrexham had the better of a goalless first half then took the lead when the impressive Mark Jones struck home a superb shot from just outside the box.
But Barrow levelled when Sam Russell parried Andy Bond's shot and the ball went in off Ashley Westwood.
Paul Rutherford set up Chadwick for a winner from outside the box before Wrexham had Mansour Assoumani sent off.
The defender received a straight red card in injury time for a late tackle on Edwards to complete a miserable day for the Dragons at Holker Street.
Barrow, who had lost five of their previous six in the league, climb above Eastbourne Borough and are now one point clear of the relegation zone.
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Wrexham manager Dean Saunders:
"The first goal is an unbelievable error by the goalkeeper and then Ashley [Westwood] kicked it in his own net.
"The second goal, Sakho's given the ball away in front of his own goal and the lad's whacked it in.
"I'm dumbfounded by the whole thing.
"The harder we try, the more difficult it seems to get and the less luck we get."
Barrow: Deasy, Spender, Jones (Pearson 34), Bolland, Edwards, Wiles, Hulbert, Bond, Rutherford, Walker (Chadwick 68), Blundell (Brown 68). Subs Not Used: Tomlinson, Boyd.
Booked: Bolland.
Goals: Westwood 67 og, Chadwick 76.
Wrexham: Russell, Spann (Obeng 63), Westwood, Assoumani, Mike Williams, Jones, Fleming, Smith (Wolfenden 82), Baynes (Holden 75), Mangan, Sakho. Subs Not Used: Taboubi, Neil Taylor.
Sent Off: Assoumani (90).
Booked: Mangan, Spann, Holden.
Goals: Jones 62.
Att: 1,066
Ref: Jeremy Simpson (Lancashire).
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