John Sheridan's struggling charges took the lead after 15 minutes when skipper Michael O'Connor curled the ball into the far corner of the net following a short corner routine.
The Magpies were dominant and could have added to their opener on a number of occasions, but Vadaine Oliver and Genaro Snijders failed to score from good chances.
However, the hosts equalised at the Hive on the half-hour mark when John Akinde turned inside the box and forced a save from Adam Collin, before Bira Dembele drilled home the rebound.
Luke Gambin then put the Bees ahead in the 64th minute with a deflected effort and claimed his second, and his side's third, ten minutes later by crashing into the top corner on the run.
Notts did not give up, with Jonathan Forte scoring from close range in the 77th minute to make it 3-2, but it was too little too late for the visitors.
The result puts the Magpies 19th in the League Two table, four points above the drop zone.
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