It was Barnet who had the first chance of the game, Antonis Vasiliou raced down on goal but he dragged his effort wide two minutes in.
However, the visitors took an early lead in the fourth minute when Alf Mason latched on to a loose ball before placing the shot high into the top left.
Ten minutes later and Barnet were given the chance to level the game when Dimeji Adeniran was hauled down in the box.
Up stepped Vasiliou who coolly finished low into the bottom right, sending Jarvis Monk the wrong way.
The Young Bees added a second another ten minutes on, Rio Connell making a good run down the left, crossing in for Okem Chime to place home.
After the break, Barnet had several chances to put the match beyond doubt and on another night the scoreline could have been much different.
Chances came and went for Chime, Adeniran, Connell and Murphy which allowed Bishop’s Stortford to rally and look for an equaliser.
Aymen Azaze pulled off two great stops to deny Bennett and spectacularly stop Mason’s curling effort from nestling in the top left.
The Young Bees did eventually put the game beyond doubt when Vasiliou cut through the defence before putting a tidy finish past Monk.
Barnet will face a trip to either Peterborough Sports of Walsham-le-Willows in the First Round Proper.
Barnet – Azaze, Pascal, Box, Tompkins, Titchmarsh, Pauw, Vasiliou, Taylor, Chime (Murphy 61), Adeniran (Addo 61), Connell
Unused – Moore, Hercules, Omore