Young defender Dan Martin was named man-of-the-match following a competent display and, above all, for the game's only goal.
It came as early as the tenth minute as Notts started really brightly and penned Barnet back in their own half.
The visitors conceded a free-kick wide on the left when skipper Nicky Bailey brought down Jake Sheridan. Lewis McMahon, always dangerous with set pieces, floated the ball into the box when Martin's glancing header flew past visiting goalkeeper Ross Flitney.
If the supporters fought they were in for a rare goal glut Barnet soon changed their minds as they came into the game with some dangerous attacks of their own.
Notts always looked solid at the back, but twice they gave chances to Barnet's front man Liam Hatch who was unlucky not to find an equaliser.
On the first occasion, with a free header, he headed wide when Notts goalkeeper Kevin Pilkington was poorly positioned.
It was an even closer call two minutes before half time. Hatch delivered a powerful header from the edge of the box and, with Pilkington stranded, Notts skipper Julian Baudet heroically cleared off his own goal line.
Following through on Hatch, Pilkington bundled the striker to the ground but strong Barnet appeals for a penalty were ignored by referee Michael Jones.
The official had another testing moment in the second half when Chris Palmer handled the ball. The decision this time was that the offence had occurred right on the 18-yard line and Notts easily survived the free-kick when Barnet felt again they should have had a penalty.
Paulo Vernazza fired over with Barnet's last chance moments after Notts had squandered a guilt-edged opportunity of an underserved second goal. Substitute Steve Scoffham put through Andy White who, with a goal at his mercy, trod on the ball.