Barnet took the lead in just the 6th minute, Ruben Bover curling a shot from the edge of the box low past Josh Knight into the bottom left corner.
Bover then forced Knight into a great close range save before doubling his personal and Barnet’s tally.
A free kick 25 yards out close to the right hand touch line was whipped in with pace before being sliced by an Enfield defender and nestling in the bottom corner.
In the 22nd minute, Barnet were awarded a penalty which Nana Kyei converted despite Knight’s best efforts.
Bover almost bagged a first half hat-trick when he struck the upright from a free kick before Nana Kyei fired over the bar from a tight angle.
Just before the break, Mauro Vilhete had an effort sensationally cleared off the line by Joe Johnston.
Enfield came at Barnet after the break and pulled a goal back in the 68th minute through Luke Thomas and set up a nervy finish when the referee awarded a penalty for a Roy Syla handball.
Harry Prince converted but right after the restart, Malakai Mars raced down on goal and bagged a fourth for the Bees.
BARNET – R. McKenzie-Lyle, Pascal, Hernandez, Sule (Coker 68′), Payne (c), Smith, Vilhete (Adinna 67′), Bover (Syla 68′), Mars, Mason-Clark, Kyei.
Unused – Busby, Shomotun