The Bees nearly got off to a flying start when, with just 15 seconds on the clock, Anthony Thomas found himself in a shooting position just outside the box. Gavin Ward in the visiting goal spilled the shot, but Wrexham cleared the danger.
However, despite having a bright start, the visitors in desperate need of a win to boost their chances of beating the drop, slowly began to get into the game with Matt Done seeing his goalbound shot brilliantly blocked by a Barnet defender.
What transpired after that was a drab affair which was only brought to life when with five minutes of the half remaining the hosts came desperately close to breaking the deadlock.
However, from Josh Wright's corner, Bees captain Ismail Yakubu saw his downward header cleared off the line by Wrexham's Simon Spender.
Barnet were though getting closer and having seen Thomas been denied after being slipped through by Albert Adomah, did go in front in first-half stoppage time. Nicky Nicolau delivered the free-kick in and Yakubu rose the highest to head home.
Once again, they flew out of the traps and doubled the lead in the 51st minute thanks to an inventive overhead kick from Thomas, which gave Ward no chance.
However, just as it seemed Barnet would have a comfortable afternoon of it, Wrexham pulled one back four minutes later when Drewe Broughton headed in Gareth Evans' free-kick.
Nicolau restored the two-goal lead, having been set up by Thomas, though Wrexham hit back again when Spender fired in a fine low strike to give them renewed hope.
Although Wrexham looked to force an equaliser, Barnet can count themselves desperately unlucky not to have wrapped the game up, as Adam Birchall struck the post, with substitute Kieron St Aimie also hitting the woodwork twice.