The Dutch player/manager received a straight red card for elbowing Stephen Wright who was also dismissed following a mass brawl in the 89th minute.
Anthony Acheampong gave the Bees an early lead but Dan Keates curled home a stunning free-kick in the wake of Davids’ red card before Johnny Hunt became the third man to be sent off following a horrific challenge on Curtis Weston.
With Elliot Johnson, Andy Yiadom and Jordan Brown all unavailable Jack Saville, David Stephens, Davids and Acheampong started at the back.
Luisma Villa also started forming a trio with Keanu Marsh-Brown and Keiron Cadogan behind new loan signing Dani Lopez.
It took the Bees just six minutes to open the scoring with Acheampong heading home a superb cross from Jack Saville.
Wrexham responded well and Graham Stack needed to be on his toes to deny Keates and Jay Harris in quick succession.
However it didn’t take long for the Bees to regain control and they might of been awarded a penalty when Marsh-Brown’s shot hit an arm in the box.
Defender Saville came closest to giving the Bees a two-goal lead when his thumping header hit the underside of the crossbar before Weston was denied on the line.
Following the break Barnet failed to maintain their impressive performance levels and Wrexham edged their way back into the game.
Joe Anyinsah had two efforts block before Stack denied Keates and Villa scrambled the ball to safety.
The closest the Bees came in the second-half was when new loan signing Lopez curled an effort towards the top corner where Coughlin tipped the ball around the post.
With one minute remaining Iffy Allen, who impressed during a brief cameo, conceded a free-kick on the edge of the Barnet box which resulted in a 20-man brawl breaking out.
Davids and Wright were subsequently sent-off before Keates curled the free-kick beyond Stack and into the top corner.
With six minutes of time added on the drama was nowhere near over as Hunt became the second Wrexham player to be sent-off following a horrific challenge on Weston who left the field of play on a stretcher.
Barnet pushed forward in the final minutes and they could have sealed all three points but Mauro Vilhete was denied by Coughlin and Stephens somehow headed wide from six-yards.
The result means Barnet are now unbeaten in four but what is perhaps concerning for the Bees is unavailability of a host of players through injury and suspension.
Barnet: Stack; Acheampong, Stephens, Davids, Saville; Casabella (Abdulla 45), Weston (Vilhete 90); Villa (Allen 74), Cadogan, KMB; Lopez.
Barnet substitutes: Jupp, Mengerink.
Wrexham: Coughlin; Carrington, Artell, Wright, Ashton; Harris (Hunt 89), Keates, Clarke; Anyinsah, Bishop (Bailey-Jones 62), Ormerod (Tomassen 90).
Wrexham substitutes: Mayebi, Ogleby.