Barnet 1-2 Exeter
Jamie Cureton struck twice as Exeter saw off Barnet, who remain bottom of the Football League and without a win this season.
Cureton opened the scoring before the break when he finished past home goalkeeper Sam Cowler after being picked out by John O'Flynn.
And Cureton doubled the advantage when he latched on to Tommy Doherty's clever pass and slotted home.
Jake Hyde headed in a consolation for the Bees late on but it was not enough.