Ten men Consett grabbed the points after what can only described as a scrappy game with Aristote Guerin-Lokonka firing in the winner in the 62nd minute.
Terriers coach Tony Burgess described his sides performance as lacklustre without a spark.
The opening half was a dull affair with neither side able to take control, the first chance falling to the home side with Williamson and Brown well off target.
At the opposite end Consett countered with Luke Sullivan just failing to get on the end of a Michael Pearson cross. Within a minute it was Sullivan again missing from close range.
After the break a more determined Consett began to take control, putting the home defence under a great deal of pressure and it came as no surprise when the dangerous Guerin-Lokonka broke clear to hammer a rising shot past McCafferty.
The home keeper was again in action brilliantly saving from Chapim
The Terriers worked hard to get back in the game with Williamson the main threat. However, there was no denying ten men Consett who should have added a second when Chapim picked up a left wing cross to take the ball past the advancing McCafferty only to see his effort hit the upright.
A late surge by Bedlington almost brought an equaliser when Mellish rose well to power a header over the crossbar.
After the match Burgess said: “At half time the players thought Consett, with only ten men, were there for the taking but they did not rise to the occasion and in the end were well beaten and could have no complaints
“We were lacklustre today and for the first time this season we failed to show the fighting spirit so it’s back to the drawing board.”
Bedlington now face two difficult matches. On Wednesday evening they take on Blyth Spartans in an NFA Senior Cup tie and Saturday they entertain Whitley Bay.