Barnet were in cruise-control throughout and it was two goals from Liam Hatch which gave them all three points.
In the 59th minute, he was at the far post to meet an Ashley Carew left-wing cross to force the ball passed home keeper Michael Jones.
It then took a goal-line clearance by Silvio Spann to deny Carew from getting on the score sheet himself.
In the 69th minute, the industrious Sagi Burton put a great ball through for Hatch, but with Michael Jones getting in a tangle with one of his own defenders, the Barnet striker was first to react and put his side two goals clear.
Wrexham had a lively start to the second-half with Simon Spender finding no-one to touch his defence-cutting ball across the visitors' goalmouth.
In the first-half Spann saw visitor's keeper Lee Harrison spill his 35-yard free-kick, but again there was no-one to cash in.
In the final minute, home sub Eifion Williams had a great chance of a consolation goal but he hit keeper Harrison with the goal at his mercy.