John McGrath put the hosts ahead with a superb free-kick but the Bees hit back in the second-half through Keanu Marsh-Brown.
From there the Bees were unable to push on and a Michael Clayton brace secured Afreton the win.
Edgar Davids’ side have started matches poorly over the last few weeks and today was no different as McGrath curled a free-kick past Graham Stack on 13 minutes.
Shortly after they should have extended their lead when the powerful Jon Akinde shot wide one on one before Clayton headed against the crossbar.
The Bees made a blistering start to the second-half against Aldershot Town midweek and four minutes after the restart they were level as Marsh-Brown fired home from range.
Surprisingly that was to be the wingers last input as he was immediately replaced by Mauro Vilhete.
After pulling level Davids’ side looked to be in control but poor defending cost the Bees as Akinde powered past David Stephens and Elliot Johnson before finding Clayton who tapped the ball past Stack.
Seven minutes later the home side were celebrating once more as Clayton converted from six-yards after Stack was only able to palm a shot into the striker’s path.
The Bees made changes with Luisma Villa and Marciano Mengerink entering the fray but unlike Tuesday they were unable to help the away side get back into the game.
Next up for the boys in black and amber is a return to The Hive where they face Macclesfield Town and Salisbury City.
Barnet FC: Stack; Yiadom, Stephens, Acheampong, Johnson; Abdulla, Weston, Byrne; Gambin, Marsh-Brown; Crawford.
Subs: Luisma, Jupp, Mengerink, Casabella, Vilhete.
Alfreton Town: Atkins, Wood, Wylde, Shaw, Clayton, Bradley, Meadows, Fenton, McGrath, Akinde, Rowe-Turner.
Subs: Franklin, Westwood, Law, Wishart, Taylor.