But Barnet didn't have things all their way and it looked as if the scrappy encounter was heading for a stalemate when John O'Flynn missed a second-half penalty.
The Bees, still buzzing after notching their first win of the season at Grimsby last weekend, and got off to a perfect start when Albert Adomah jinked his way past a static Stanley defence to cross for O'Flynn to head in at the far post.
It was former Cork City forward O'Flynn's first goal for Barnet since moving across the Irish Sea in August.
Adomah was causing constant problems running at Stanley defenders, but the visitors managed to weather the early storm and battle back to gain a foothold in the game.
Skipper Peter Cavanagh was the architect of their progress, whipping in a series of crosses that threatened the Bees goal, while John Miles wasted a good chance when he found himself in space in the area but opted to pass straight to Yakubu rather than shoot.
Jimmy Ryan then had a penalty appeal waved away as Stanley grafted away and their efforts were finally rewarded on the stroke of half-time.
Miles' corner was met with a superb near post header by big defender Colin Murdock, giving Barnet keeper Lee Harrison no chance.
Stanley started the second half as they finished the first - creating chances - and Joe Devera had to be alert to scramble away Ryan's header.
But the real drama unfolded after 72 minutes when substitute Robbie Williams was given a straight red for hauling down Adomah as he bore down on goal.
Stanley thought they'd seen off the danger when Arthur pushed O'Flynn's resultant spot-kick around the post, but Nicky Nicolau's corner was headed in by Yakubu.
Stanley players were crestfallen and Barnet held out easily to grab the win.