Celtic succumbed to their second defeat on the trot, whilst Alfreton marched on with their 7th successive win.
As in the last few games, Celtic started strongly, and could have altered the course of the match when Caldecott nipped in to steal the ball off Brown's feet and lob a ball into the path of Foster. From just outside the box Celtic's top striker curled a powerful driven ball past Butler and into the base of the post.
The game was finally balanced until half an hour in, when Alfreton made the breakthrough. Goddard's cross was met by Godber, and the 'God-Squad' as the pair are known, continued their scoring spree with Dootson left the unlucky recipient of the defence opening just enough for Godber to have the time to pick his spot.
Celtic responded with a lot of crosses into the box from both Bowman and Caldecott, but were having no luck in breaching the defence.
When Bowman conceded a free kick some thirty yards from goal, Bradshaw caused consternation in the Celtic defence, with the clearance - if it could be called that - falling onto the sweet right foot of Godber, whose shot rocketed through the packed area into the bottom corner.
Celtic once again were looking for ideas and inspiration, and coming up with nothing but long distance shots, and ball chasing, with Bowman getting the closest, actually forcing Butler into a save.
Atherton were causing no end of trouble, and Dootson twice came to the rescue blocking a Goddard volley and a Godber toe-poke.
With Foster chasing shadows, he was replaced by Fitzgerald, and Celtic consolidated. They remained shaky but solid until just before the death when a Town corner was lifted to the near post for Bradshaw to nod home and leave the Celtic defence looking sheepish.
And so it should have ended, but from somewhere, Parr gave Celtic a modicum of pride by placing a superb header from a corner into the corner a couple of minutes into injury time.
Celtic's performance was not the performance that everybody knows that they are capable of, and the fans were left feeling a little disappointed. The whole team could benefit from an injection of enthusiasm.