Kenny Gillet received his marching orders after just 13 minutes for a nasty challenge on the lively Chris Turner.
But by that time veteran striker Paul Furlong had already given the visitors the lead, heading home Albert Adomah's cross as early as the sixth minute.
Accrington have struggled at home all season, only gaining 15 points in East Lancashire prior to this game.
And they struggled to get a foothold in this game until their top scorer, Paul Mullin, struck ten minutes into the second half to ensure the three-point gap between the two sides remained intact.
The burly Stanley skipper, who typifies Accrington's robust style of the play perfectly, converted Turner's delivery into the middle of Ran Kadoch's goal from close range.
The hosts piled on the pressure in the final half hour, but could not grab a second for what would have been just their fifth home win of the campaign.
While Barnet will be pretty pleased with a point away from home, especially after they were reduced to ten men for the vast majority of the game, this result does not do either side any favours in their attempts to escape the lower reaches.