After an uninspiring opening 20 minutes, the visitors then began to enjoy the better of the play.
They felt they had a penalty shout when Bees skipper Sagi Burton slid in on Simon Brown only for the referee to point for a corner and then they spurned two gilt-edged chances.
First, Michael Boulding raced clean through only to be denied by Lee Harrison in the home goal, before Stephen Dawson's cross into the box was met by Johnny Mullins at the far post, but he somehow headed it back across the face of the goal when it seemed easier to have scored.
However, they didn't have to wait long to get in front as just 90 seconds into the second half, goalkeeper Carl Muggleton's long kick forward was flicked on by Boulding into the path of Brown who struck low past Harrison.
Stung into action, the Bees had a glorious chance to get back on level terms through substitute Lee Hatch.
However, had he of converted from six yards out it would have caused a near riot as the attack came as a result of Barnet not giving the ball back after Mansfield had kicked it out of play for an injured player.
But there was no controversy in the 71st minute when he fired in from eight yards out after being neatly set up by Adam Birchall.
They had the chance to go ahead through Jason Puncheon after Boulding handled the ball in his own box, but 39-year-old Muggleton produced a fantastic save to turn the ball onto the underside of the bar.
Barnet pressed for a winner and came agonisingly close in the 90th minute when Ashley Carew's shot took a wicked deflection off a Mansfield defender but hit the foot of the post.