Two goals in the opening seven minutes set Barnet on their way in the North-East and put them on course to record yet another win during the opening months of the campaign.
The Bees continued to press as the half progressed with John Akinde and Lee Cook both going close for the visitors, while Gateshead offered a brief reply before the break when Michael Rankine brought a comfortable save out of Graham Stack.
Barnet applied more pressure at the start of the second half, with Cook seeing a free kick deflected over the crossbar and Villa being denied inside the penalty area by Adam Bartlett.
Mauro Vilhete was the next Barnet player to try his luck but after creating space for himself on the edge of the area, he blazed the ball into the stands.
However, Barnet managed to weather the storm to strengthen their position at the Conference Premier summit.