In the absence of the sidelined player/managerEdgar Davids, Barnet had their chances in the first half but Reid's spot-kick soon after the interval, followed almost immediately by a straight red card for Jon Nurse, put paid to their chances.
Barnet started sluggishly, but it they forced the game's first save as Jamie Young reacted smartly to palm Ricky Holmes' drive round the post.
And with 30 minutes played the Bees should have taken the lead but, after Nurse saw his strike clawed away, Barry Fuller screwed the rebound wide of the near post.
At the other end, Reid twice went close in a matter of seconds but after the break he made no mistake, slamming home from the spot after Sonny Bradley's drive was handled in the area.
Nurse then got his marching orders for a dangerous challenge on Dani Lopez but the hosts nearly snatched an equaliser when Jake Hyde was ruled narrowly offside as he bundled in Holmes' near-post centre.