The visitors dominated the early exchanges and fired a warning to the home side after just two minutes when Gavin Heeroo volleyed just over the bar.
The Boro defence looked unable to cope with the pace of Courtney Pitt and the height of Fola Onibuje and it was the pair who combined to put Cambridge ahead on seven minutes.
Onibuje used his physical presence to win the ball in the box, guided a pass to Pitt which he drove in thanks to a deflection off Rob Quinn.
With the home defence looking nervous Cambridge had further chances and their best effort came on 20 minutes when Dave Bridges guided a powerful header just past the post from a corner.
Stevenage edged their way back into the match and it was the talented George Boyd who proved their inspiration. Boyd forced a stunning save from Cambridge keeper Scott Howie midway through the half and from the resulting corner Ronnie Henry saw a goalbound header cleared off the line by Bridges.
Stevenage continued to press forward and got the equaliser they arguably deserved two minutes from the break when Howie spilled a long-range drive from Michael Warner and Jon Nurse reached the ball first to head in.
The home support were then sent into dreamland two minutes into added time when Boro went into the lead courtesy of a long-range shot from Jefferson Louis which was set up by Boyd.
With the whole complexion of the game changed Stevenage began the second half in confident mood and they grabbed the decisive third on 56 minutes when a sweet pass from Williams found Boyd 25 yards out and saw the Stevenage midfielder crash home a stunning volley to sink Cambridge.
The visitors were unable to hit back and couldn't muster a shot on goal in the second half.
Indeed it was Stevenage who looked likely to extend their lead with Dino Maamria seeing a header come back off the post after a Danny Williams cross, while Dannie Bulman tested Howie with another spectacular volley which the goalkeeper this time was able to keep out.