Wrexham came up short against a Barnet side who collected the points thanks a late strike from Jake Hyde.
The forward’s goal on 78 minutes fired the Bees back into the play-off places.
The home side enjoyed the better of possession in the opening period, but were unable to take their chances, which included a great save by keeper Nick Jupp to deny Joe Clarke.
Andy Bishop twice went close in the first half and Danny Livesey scooped a set piece back into the danger zone, but it was then cleared.
The second half was a much more tepid affair as Wrexham failed to worry the visitors and paid the price.
Hyde was thwarted at the other end before he hit the target from close range to earn the Bees a fourth consecutive victory.
The Dragons now head to Luton Town on Tuesday night with the Hatters being the ones who are breathing fire at the moment.
Wrexham: Andy Coughlin, Mark Carrington, Danny Livesey, Steve Tomassen, Neil Ashton; Joe Clarke, Jay Harris, Dean Keates; Elliott Durrell (Kevin Thornton 80), Andy Bishop (Rob Ogleby 70), Joe Anyinsah (Brett Ormerod 63).
Subs: David Artell, Johnny Hunt.
Barnet: Nick Jupp, Dave Stephens, Valentin Gjokay, Elliot Johnson, Curtis Weston, Kieron Cadogan, Charlie Adams (Roberto Casabella 82), Andy Yiadom, Mark Byrne, Keanu Marsh-Brown (Dani Lopez 67), Jake Hyde (Marciano Mengerink 90).
Subs: Ahmed Abdulla, Mauro Vilhete.
Referee: Ross Joyce (Teeside)
Wrexham: Harris (foul)
Barnet: Yiadom, Weston, Byrne, Cadogan