Adam Cunnington scored the only goal as Cambridge extended their unbeaten start to the season by beating 10-man Hyde.
Cunnington put the U's ahead when he nodded in Ryan Donaldson's free-kick from close range.
Mitch Austin went close to doubling Cambridge's lead after the break when he fired Nathan Arnold's cross wide.
The hosts were reduced to 10 men late on when Liam Tomsett was sent off after being adjudged to have elbowed Cambridge keeper Chris Maxwell.
VIEW FROM THE DRESSING ROOM
Cambridge United boss Richard Money told BBC Radio Cambridgeshire:
"It was a hard-fought victory as I knew it would be. They're good with the ball and they tested our organisation. Thankfully it stood firm and we were able to get the goal that mattered.
"Those that gain trophies at the end of the season are the teams that can win when they are not at their best and today was one of those.
"We weren't good enough to get a second goal today - that's the truth. But we were good enough to get the three points. In a month or two we'll forget about the game and think about how many points we picked up here."