Second half goals from Danny Haynes and Matt Sparrow proved decisive after the visitors had cancelled out an early Shaun Harrad strike.
That goal came after just 80 seconds, Hayes the provider as he slid a pass into Harrad’s path for the striker to power his shot beyond keeper Chris Dunn.
Cheltenham continued to dominate and Zack Kotwica crashed a glorious 25-yard effort against the post on the half-hour. Mathieu Manset tucked away the rebound but from an offside position.
Cambridge offered little in attack but still managed to level in the 34th minute when Ryan Bird swept home a Dominic Ball cross.
But the second half belonged to the home side as they wrapped up the points in style.
Haynes swept in in the 57th minute after skipper Matt Taylor had headed a corner back into the area.
And the points were in the bag when, with 15 minutes to go Matt Sparrow’s 25-yard effort was deflected over luckless keeper Dunn.