Danny Allsopp should have done better with a lob after 13 minutes, and Marshall again saved to deny the Australian from 6 yards.
But the forward maintained his record of scoring in every league game since signing from Notts County by making it 2-0 with 20 minutes on the clock. He battled to reach a ball down the middle on the edge of the box and knocked it round the keeper before retrieving it to tap into the empty net.
Paul Musselwhite - again deputising for Alan Fettis - made a good save from Luke Guttridge's 20-yard effort to keep the score at 2-0 at the break.
Early in the second half City had a good chance when Dean Keates was brought down on the edge of the area, but Stuart Elliott wasted the free kick.
Damien Delaney cleared Dave Kitson's shot off the line with Musselwhite beaten, and Cambridge didn't look like upsetting a City side desperate for 3 points.
Danny Allsopp had another chance late on, while substitute Andy Holt put in an industrial performance but no further goals were to come, so Peter Taylor's side got the win they deserved.
City line-up (4-4-2): Musselwhite; Thelwell, Whittle, Hinds, Delaney; Price, Ashbee, Keates (Melton 77), Elliott (Holt 77); Burgess, Allsopp.
Un-used subs: Green, Webb.