A goal from forward Sam Hoskins has given Barnet a 1-0 half-time advantage against Eastleigh.
The Conference Premier leaders almost took the lead with just 60 seconds on the clock but Hoskins, who is on loan from Yeovil Town, struck the post with a half-volley.
Barnet continued to have the better of the play but Eastleigh, who have recently fallen down the standings after a bright start, were starting to threaten up the other end of the pitch as the half reached the midway point.
Michael Green and Jamie Collins both squandered chances shortly before the half-hour mark for Eastleigh, and they were made to pay as Barnet took the lead with eight minutes remaining.
The ball fell to Hoskins, whose deflected effort from the edge of the penalty are found the bottom corner for his second goal of the campaign.