A hat-trick for midfielder Jason Price last week was followed by a brace from his left wing counterpart Stuart Elliott this week.
Cambridge were hesitant from the off, and City tried to exploit their edginess, having most of the possession in Cambridge's half.
After six minutes, an easy shot from Jamie Forrester was saved, but although City were by far the sharper, they couldn't carve out any clear cut chances.
After 20 minutes, a 20-yard shot from Ben Burgess went just over, but a minute later John Taylor responded with a similar effort at the other end.
On 22 minutes Andy Dawson saw his shot saved, and after the half-hour mark Burgess and Elliott had chances in the box before Shaun Marshall saved Price's header after a moment of panic in Cambridge's defence.
On 42 minutes, the Tigers dominance paid off when Elliott picked up the ball on the left wing - where he had been working hard and providing excellent crosses all half - and he eluded marker Stevland Angus and blasted a 20 yard shot under the keeper.
Just after the restart Price's shot was kicked around the bar, and from the corner, Burgess saw his header somehow kept out by Marshall.
On 55 minutes a rare attack by Cambridge saw Dawson cut out a dangerous cross by Angus. But seconds later an excellent ball from Ian Ashbee put Burgess clear and he had acres of time to shoot over Marshall, but his shot bounced agonisingly off the crossbar.
Moments later Forrester shot wide, before Price had a header easily saved.
City made it two in the 59th minute when Elliott raced clear again down the left, and slammed a goal almost identical to his first.
A few minutes later Fred Murray got Cambridge's first shot on target after a momentary lapse in the Tigers' defence, with Boaz Myhill doing well to tip away before it was cleared off the line.
But there was no stopping City's relentless attack, with Cambridge's manager Taylor dropping himself into the back four to shore up his defence.
But it was to no avail and they will have been relieved when defender Marc Joseph saw his goal disallowed for offside in added time.