The Shakers took the lead after 23 minutes through captain Nathan Cameron, who drilled the ball low across goalkeeper Chris Dunn following Danny Mayor’s cross from the left.
The U’s had come close to taking the lead within the opening moments as Ryan Donaldson let fly from nearly 30 yards and forced a tremendous tip-over save from Nick Pope.
Bury dominated after taking the lead with Tom Soares forcing Dunn into a low save, Andrew Tutte being denied by a Josh Coulson challenge and Mayor hitting an effort from outside the box that Dunn did well to push away.
The advantage was doubled eight minutes into the second half when Tom Champion misjudged a through ball, allowing Mayor to feed Soares who drove a finish beyond Dunn.
Sullay Kaikai came closest to reducing the deficit but Pope repelled two of his efforts, leaving Cambridge only five points above the bottom two.