Barnet have impressed during the first 45 minutes against Wrexham but the game at The Hive Stadium remains goalless at the break.
The home side dominated the opening 10 minutes against their Welsh opponents, with Lee Cook and John Akinde both having efforts go close.
Curtis Weston also tried his luck from 30 yards but the visitors managed to see out the opening quarter of the game without conceding a goal.
Luisma Villa has enjoyed an impressive start to the campaign for the Bees and he nearly gave them the lead after the ball fell invitingly to him inside the penalty area, but he could only blaze over from close range.
Wes York squandered one half-chance for Wrexham, but after being on the back foot for much of the opening period, they will be relieved to be on level terms.
