A dreary, scrappy encounter seemed to promise little in the way of entertainment, let alone any goals, until Michael Gash conjured a startling strike out of nothing in the third minute of stoppage time before the break.
Gravesend had the interval in which to re-group, but were ripped apart just two minutes after the re-start and were never able to recover to show the form which had lifted them to seventh place in the table.
It was a case of the Fleet sinking without trace or much of a struggle as the home side took over so completely they might have doubled their score.
There was no real sign of such a result during a first half which until stoppage time was only notable for a close-range miss by Gash in the tenth minute and the sickening clash of heads between United's Robbie Simpson and Gravesend's Sacha Opinel which meant a stretcher ride for Simpson in the 31st minute.
He had to have 11 stitches in a head wound, but was able to return to the ground before the end of the game.
Gash made up for slicing the ball wide from only four yards by placing a superb shot inside the far post when he turned unmarked on the ball 25 yards out in stoppage time.
It was winger Courtney Pitt who set up the opportunity the striker wasted, and he decided to go it alone in the 47th minute, racing through on the left to lift a shot over the keeper and high inside the far post.
In a bid to spark his team into some kind of action Gravesend boss and former Cambridge hero Liam Daish made a dramatic three-man substitution in the 55th minute which should have had an almost immediate impression on the match.
One of the substitutes George Purcell hit a 58th minute shot which bounced back off the foot of a post into the path of another sub Danny Ekoku who was unable to turn the ball into the net from a couple of yards out.
After that let-off Cambridge, boosted by midfielder Danny Brown on his debut after his switch from Crawley Town, regained the initiative and easily hung onto it.
It was as good as over in the 73rd minute when David Bridges put the feel on an excellent performance by running on to a perfect pass from Marcus Richardson to drive the third goal past helpless keeper Lance Cronin.
There might have been a couple more Cambridge goals in the dying stages, but Peter Hawkins just managed to deflect a Bridges shot and Pitt also went agonisingly close to a second for himself.
The attacking players stood out for injury hit Cambridge who are down to the bare bones of their squad in what was a crucial match for them after losing five times this season in front of their frustrated home fans.
But there was also a vital contribution from centre-backs Andy Duncan and Michael Morrison, who subdued the Conference's 13-goal leading scorer, Charlie MacDonald.
McDonald had run the United rearguard ragged in the season's away match in Kent, but hardly got a sniff as the centre-back partnership set out from the start to make their presence felt and in fact the defensive display was so solid that Gravesend failed to get a single shot of any real venom on target in the entire match.