The strike from Bramble was an astonishing effort, boosting confidence in the home side's ranks as they faced a Wanderers team aiming to make it five consecutive wins on their travels.
The big striker unleashed a shot from all of 35 yards which flew high inside the left hand post in the 13th minute.
Poor defending wiped out the lead just four minutes later, however, when Gus Uhlenbeek followed up a series of blocked attempts and slid a shot in from close range.
But with Roberts alongside Bramble, United always looked a threat and the former Norwich hero used all of his experience just before half-time, when he turned a poor corner kick from Justin Walker into a good one by clipping the ball inside the near post.
Wanderers went all out to maintain their impressive away record laying siege to the Cambridge goal after the break.
But United, inspired by centre-back Adam Tann and Andrew Duncan held firm as Wanderers' star striker Nathan Tyson had a bit of a nightmare.
He was twice clear after racing through the middle only to fail to hit the target, and five minutes from time he headed against the crossbar from six yards, his embarrassment eased by an offside flag.
Cambridge would hardly have deserved to win by more than a goal in an enthralling tussle, but Shane Tudor almost rounded off the battling display in front of hundreds of supporters from around the country on a Fans United day by blasting a shot against the crossbar just before the whistle.