The Wales under-21 international had an easy tap in after Paul Linwood started a move and Jon Walters played a neat pass into the six-yard box to give Barnet stopper Scott Tynan no chance.
Giuliano Grazioli should have levelled when he was clean through but home keeper Mike Ingham made a fine save and later the Barnet striker missed a sitter by firing a 20-yard shot wide with the keeper stranded.
Next it was the turn of Walters to shoot wide of an open goal and Alex Smith also missed a good chance.
Paul Warhurst put Wrexham further in front after Darren Ferguson's corner was tapped on by Robbie Foy.
Ferguson just missed making contact with a header from a fine cross by Foy and from a Ferguson corner Danny Williams headed over the bar.
A mistake by defender Dennis Lawrence handed Barnet a lifeline just on half time when his heavy push on Dean Sinclair gave away a penalty that Ian Hendon aimed a little close to the keeper who got a hand to it but helped it into the net.
Barnet looked stronger after the interval and Sinclair was out of luck with a 15-yard shot that whistled past the post.
Richard Graham also missed when he might have put the Bees back into the game.
A superb move started by Jones gave Wrexham their third goal as Foy smashed a 25-yard shot into the top corner on 59 minutes.