They battered the sixth-placed team, creating more than half a dozen scoring chances in the first 40 minutes as they pinned the visitors in their own half.
David Bridges struck in the 19th minute for the goal that gave Cambridge three thoroughly deserved points, but they should have had a lot more goals.
Striker Fola Onibuje missed a hat-trick of chances in the first 34 minutes of the match, lobbing over in the second minute, firing wide in the 16th and then somehow failing to bundle the ball in from only two yards out in the 34th.
Fellow forward Craig Westcarr showed him how to hit the target but was denied by a couple of excellent saves from goalkeeper Alan Julian.
But Westcarr contributed to the goal with a well-placed cross for Bridges to score with a flying header at the far post.
In a much quieter but more niggly second half, Stevenage almost equalised on the hour with a rare attack when Darryn Stamp fired a shot against the crossbar.
It got more bad tempered as the half wore on and, after a series of bookings, Stevenage's Ollie Berquez was red carded for an off-the-ball foul in stoppage time.
It should be a lively encounter at Stevenage on January 2nd but Cambridge, who need a run of results to move up to the play-off places, will be encouraged by their all-round display in what was, on paper, a tough test.
They were always on top in midfield where Ritchie Hanlon controlled things until limping off late in the game and had far more ideas up front. In defence Andy Duncan and Mark Peters had the strength to cope with anything a lame Stevenage attack could throw at them.