Barnet remain in the League Two relegation battle despite beating play-off-chasing Bradford 2-0 at Underhill.
James Hanson shot wide early on for the Bantams, who play Aston Villa in the first leg of their Capital One Cup semi-final on Tuesday.
Taiwo Atieno tapped in Elliot Johnson's first-half cross to score his first goal since joining the Bees last month.
Nahki Wells missed a great chance to level and the Bees counter-attacked with John Oster adding the second.
VIEW FROM THE DRESSING ROOM
Barnet manager Edgar Davids told BBC London 94.9:
"I'm very happy that we got the three points and with the way we accomplished that.
"I saw some very good spells and it makes you happy to be a part of it.
"They have a very direct style and it was very hard to fight against them.
"We also went for the direct approach but kept the ball on the ground."