Charlie Barnett and Kevin Long both saw red for Accrington in a fiery encounter against Barnet but Stanley still held on for a point from a goalless draw at Underhill.
Accrington were reduced to 10 men just before the break when Barnett received his marching orders for a reckless two-footed lunge on Bees striker Steve Kabba.
However it was the visitors who came closest to scoring through Luke Joyce and Ian Craney before 10 became nine when Long was dismissed for holding back Charlie Taylor late on.
Barnet began the match on top and could have gone ahead five minutes before Barnett's red card as Kabba pounced on a long kick from Dean Brill.
The 30-year-old barely stung the hands of Sean Murdoch, though, before being involved in the incident surrounding Barnett's dismissal.
Accrington responded better than Barnet and Brill was called into action to stop a 20-yard free-kick from Joyce moments later before Craney powered wide in the second half.
Barnet were struggling to find a way through and, despite Long seeing red for hauling down Taylor while through on goal in the dying seconds, they had to settle for a point.
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