Their outstanding success at Cardiff in the Carling Cup earned them a trip to Leeds which manager Paul Fairclough said could be one of the highlights of their season.
He said: "This has capped a great week. It is a great opportunity for the club and a wonderful journey for my players."
Wrexham started strongly and took an early lead and it was again Mark Jones in the spotlight, when Anthony Charles dispossessed Chris Llewellyn the ball ran free for the young midfielder to crash it in from long range.
A curling 25-yard shot from Mark Jones six minutes later nearly caught out Barnet keeper Lee Harrison and sent him back-pedalling to tip it away for a corner.
Another free-kick from Matt Crowell was headed down by Steve Evans and deflected for a corner which Barnet defenders scrambled clear.
Again, from another Crowell free-kick, Evans headed down and wide.
At the other end Barnet went close from Ian Hendon's free-kick which Giuliano Grazioli hooked back across goal and Tresor Kandol saw his header touched on to a post.
Barnet came back into the game and from a deep corner floated in by Jason Puncheon, Nick Bailey got in a low header that Mike Ingham went down to save.
Hendon was withdrawn at half-time with a toe injury, being substituted by former Wrexham player Paul Warhurst, manager Fairclough later pointing out it had nothing to do with the crowd barracking Hendon for a couple of tackles earlier in the game.
A goal seemed on the cards and it came when Barry Cogan crossed from the right and Kandol got to it ahead of Grazioli to head in at the back post completely unmarked.
Then Kandol headed back across goal from a Puncheon cross giving Wrexham a fright as it was cleared for a corner.
Grazioli netted with his next header from a Cogan corner, only to have his goal disallowed for a foul on the keeper.
Wrexham made three late substitutions to bring on fresh legs and substitute Jon Newby saw a shot tipped for a corner.
Barnet substitute Jason Norville also came close to getting a winner with a shot that Crowell hacked off the line.