Ryan Crowther secured Hyde's first Blue Square Bet Premier away win of the season at the expense of Cambridge.
Tom Elliott went close for the home side but he headed Robbie Willmott's cross over the crossbar.
Crowther picked out Scott Spencer for the best chance of the first half but the striker could only head past the post from six yards out.
And it was left to Crowther to steal the points late on when he crashed in a 20-yard effort via a slight deflection.
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Cambridge United first-team coach Richard Money told BBC Radio Cambridgeshire:
"I thought the first half was a good game. In my five games, that is the best performance I've seen against us and they played well.
"We started the second half sloppy, the crowd got frustrated and disappointed but the players have to understand it's really based at me.
"I'm the guy in charge, I'm the guy that puts it on the pitch and I accept the frustration."