A scrappy game with few chances was snatched late on by the hosts through a single Danny Kedwell strike.
The Bees had the first opportunity of the game when Harrison’s volley from Taylor’s corner was saved two minutes in.
Cheek had a cross blocked by Sweeney at the other end before a barrage of rain really changed the game, making it difficult for either team to create a chance.
The rain would ease after the half hour and Sweeney was in the right place in the right time to clear Ebou Adams’ free kick.
With virtually the last kick of the first 45, Whitely fired over from the edge of the box.
Barnet came out with more urgency after the break, Bettamer forcing Ashmore into a low save in the 46th minute after getting around the Ebbsfleet defence.
On the hour, near interplay between Johnson and Fonguck allowed the latter to get a shot off but it pooped just over the bar.
Jack Taylor hit the side netting which culminated the Bees best spell of pressure.
McDonald’s half volley was dragged wide of the left hand post before Fonguck forced a comfortable save from Ashmore.
McDonald had a similar chance minutes later but again shot wide.
Bettamer cut inside onto his left in the 75th minute, had a chance to shoot but didn’t, fed Johnson but his shot was blocked.
The deadlock was broken in the 84th minute when Kedwell got on the end of the ball over the top, had plenty of time to pick his spot and finished calmly past Cousins.
Barnet mounted additional pressure after the goal, which almost allowed McDonald a chance to score on the counter but Cousins made himself big to save.
With the last opportunity, Fonguck’s low shot forced Ashmore to scramble down to his right to keep it out.
Barnet: Cousins, Alexander (Elito 43) Johnson, Reynolds, Robson, Adams, Harrison (Coulthirst 64), J. Taylor, Fonguck, Sweeney, Bettamer (Mason-Clark 85)
Unused – Matrevics, Sparkes