The Bees were dominant in the opening quarter but with 25 minutes played Andy Yiadom was sent off.
Three minutes later the home side took the lead but KMB’s thrusting run won a penalty midway through the second-half and he remained cool to slot home.
The hosts made a bright start to the match but after Ross Lafayette was forced off through injury on six minutes Barnet took control.
Kieron Cadogan, who made his first appearance for the club, created the first chance of the match, turning excellently on the edge of the box before shooting just wide.
Just one minute later he was again inches away from scoring as Mauro Vilhete smashed the ball across the face of the goal where the winger was just unable to connect.
On 13 minutes Yiadom almost got his second in two matches but his low shot was deflected behind for a corner, from which Jake Saville headed against the crossbar.
Six minutes later the home side were almost gifted the lead when Edgar Davids’ wayward back-pass trickled just wide of the post.
The Bees continued to press but their dominance continued to go unrewarded as Marciano Mengerink saw his header cleared off the line.
Two minutes later the Bees dealt a huge blow when Yiadom received a straight red card.
The decision, which looked very harsh, changed the game and four minutes later the hosts took the lead in comedic circumstances as Joe Healy’s scuffed cross looped over Stack and into the net.
Despite being a man and a goal down the Bees remained positive and goalkeeper Lee Butcher ensured their lead remained in tact by denying Marsh-Brown from range on two occasions.
The Wings could have doubled their lead just three minutes after the restart when Alex Dyer fired over from just ten-yards.
Thankfully the Bees made the home side regret wasting that golden opportunity as Marsh-Brown won and converted a penalty with 18 minutes to play.
Further positives followed for the Bees as Jake Hyde made a return from injury.
Welling did go close to a winner in the closing stages when Kiernan Hughes-Mason hit the post but the Bees hung on for a deserved point.