McManus and Cisse put through their own net either side of a Jonathan Stead strike for the hosts, who huffed and puffed tirelessly without any luck.
Cardiff took the lead in the final minute of the first half, with McManus inadvertently poking past David James after Joe Mason sent a fizzing low cross into the Robins' penalty area.
After the break the home side had to withstand seven minutes of intense pressure, with James making three good saves, before Stead levelled.
Following a relatively incident-free first half, the second period then sparked to life.
Aron Gunnarsson and Kenny Miller had great chances to restore Cardiff's lead, while Sean Davis tested David Marshall at the other end and Brett Pitman struck a post for the hosts.
But Mason's centre, with three minutes left, bounced off Cisse's knee and beat James to lift Cardiff back to sixth and leave City struggling.
Cardiff's first chance of any note came just before the half hour mark, but James turned Miller's rasping half-volley out for a corner.
A scrappy game seemed to be meandering through to half-time goalless, after Stephen Pearson wasted a glorious chance to put the hosts ahead in first half stoppage time.
Stead's cross was not properly cleared by the Cardiff defence and when the ball fell to Pearson just inside the area the midfielder should have done better than blaze over.
And the Robins were made to pay for the miss, as the visitors stole the lead in the final action of the first period.
Mason fired in a low cross from the right, McManus stuck out a leg and the home defender could only divert the ball past his own keeper.
Early in the second half, Miller neatly turned Liam Fontaine only to shoot tamely into James' arms before the City stopper produced a good stop low down to his left to keep out Gunnarsson's fierce volley.
And the Icelander was denied by James once more moments later, pushing his long-range effort over the crossbar as the visitors pushed hard for a second goal.
But it was the home side that struck next.
Ricky Foster danced down the right wing, pulled a lovely cut-back into the path of Stead and the striker buried the chance in off Marshall's left post.
Buoyed by the equaliser, the home side began to put together good passages of possession, and at the end of a swift move substitute Sean Davis' curling effort produced a decent stop from Marshall.
The match was picking up pace, and only a brilliant last ditch tackle from Fontaine prevented Miller form latching onto Peter Whittingham's stunning through ball with 15 minutes remaining.
At the other end, Marshall produced a sensational stop to prevent Pitman from sliding the ball home at the near post from Stead's teasing cross from the right, while Pitman struck a post from a narrow angle before Cardiff nicked it.
Whittingham found Mason in the box and the forward's cross struck Cisse and bobbled into the net, leaving James stranded and Cardiff elated.