Wrexham had won just one game away from home all season going into this game and things looked bleak when they went behind mid-way through the first half.
The Bees had the first chance inside the first 10 minutes when Jason Puncheon made a good run on the left and cut inside into the box, his powerful shot was fumbled by keeper Michael Ingham for a corner.
The home side continued to mount pressure on the travel sick Wrexham defence and in the 21st minute Richard Graham made a 30-yard run into the visitors' half but his cross failed to find in form Oliver Allen.
Allen had another chance minutes later when he flicked the ball over Mike Williams but his shot forced a good save from Ingham.
The striker's luck was in just before the half hour. Liam Hatch and Danny Williams tangled on the edge of the box and the ball broke to Allen who slotted home from 10 yards out despite the best efforts of Ingham, who managed to get a hand to it.
Wrexham had a good chance to level the scores when Simon King brought McEvilly down on the edge of the area. From the resulting free kick McEvilly hit the crossbar in what was the visitors' best chance of the half.
Dean Sinclair missed a good chance for Barnet when he failed to keep his header on target from a Puncheon cross just before the break.
McEvilly brought the Welsh side back into the game on 56 minutes with a powerful shot from 25 yards that gave Ross Flitney no chance.
Three minutes later the game was turned on its head as McEvilly grabbed his second when he headed home from six yards after a good cross from Chris Llewellyn from the left.
Allen tried to revitalise Barnet as he played in Adam Gross in the 68th minute. He beat the offside trap but could not beat an inspired Ingham who made a brilliant point-blank save to deny the home side.
Wrexham climb out of the relegation zone and Barnet sink to their second straight defeat.