It was a nightmare start for the visitors. They were just getting over an early assault on their goal from Liam Hatch when Tommy Wright was given his marching orders on 43 seconds.
The striker led with his elbow in a challenge with Bees defender Simon King, and referee Roy Lee did not hesitate in showing the red card.
And Darlington soon found themselves a goal down as well as a man down. Goalkeeper Sam Russell was forced to tip over a Nicky Nicolau free-kick which caught the wind, and from the resulting corner Dean Sinclair scored.
But the response Dave Penney's side made was first class, and they soon looked like a team of equal numbers to their opponents.
Darlington were amazingly back on level terms on the 22-minute mark when an Evan Horwood free-kick was headed home by David Wheater.
It was the defender's first goal for Darlington and his last as he returns to Middlesbrough following a short-term loan after this game.
But Barnet were always going to have the upper hand while they had their one-man advantage.
Another swirling Nicolau free-kick five minutes before half-time caused Russell all sorts of problems. He spilled the ball and a goal-mouth scramble ensued before the ball was eventually cleared.
But a Nicky Bailey set-piece seven minutes after the break proved even harder to defend, as Liam Hatch was on hand to tap home for what proved to be the winning goal.
And it could have been worse for Darlington but Russell pulled off a fine 66th-minute save from a Nicolau effort.