The Bees had a glorious chance to open the scoring after three minutes as Alfie Pavey was slipped in on goal, his strike was saved by the Dover 'keeper. Up the other end, Ahkeem Rose went through on goal but dragged his shot wide of Scott Loach's goal.
The next chance came the way of Tim Flowers' side, as good hold up play from Pavey allowed Myles Judd to strike just wide of the far post. But the next attack saw the hosts open the scoring, as Will De Havilland poked home on the rebound after Loach made an initial stop from a flicked header.
It was a carbon copy just minutes later, as the Bees were punished from another set-piece as De Havilland poked home from almost the same position to add a second goal of the evening.
It was soon three as Rose picked up a loose ball and volleyed past Loach, leaving him with no chance.
The Bees had a mountain to climb and tried to reduce the arrears immediately after half time, as James Dunne had an effort deflected behind.
It was 3-1 with half-hour left to play as half time substitute Michael Petrasso scrambled one home from a cross into the box.
Flowers' side continued to try and find a way back into the match but couldn't create any real clear cut chances, as the game became scrappy on the difficult pitch.
Dover almost sealed it with two minutes on the clock, but Loach made a fine stop with his legs before the ball rebounded onto the post.
Ultimately, the Bees left themselves with too much to do and left Kent with nothing.
Barnet: Loach, Judd, Kefalas (Petrasso 46'), Richards-Everton, Daly, Binnom-Williams, Dunne, Taylor, Mason-Clark, Pavey (Faal 62'), Hooper.