Fulham's reserve side took City's big guns to extra-time in their third-round tie at Eastlands before central defender Kolo Toure came to their rescue with an 111th-minute match-winner.
It was a measure of how seriously City were treating the cup that ten of the starting line-up in Sunday's Manchester derby kicked off against Fulham.
And it was an indication as to how low in Fulham's list of priorities the knockout clash was that they changed the complete team which played at Wolves on Sunday.
City, who had won only one of their previous six home games against Fuham, received a jolt after falling behind to a 34th-minute wonder goal by Zoltan Gera.
The Hungary international beat City keper Shay Given with a spectacular 25-yard half-volley.
City failed to trouble David Stockdale, Fulham's second-choice keeper in a lack-lustre opening period which lacked the sparkle of Sunday's absorbing Manchester derby.
The second half saw City kick-off with more purpose to their play and they were soon on level terms.
Gareth Barry popped up at the far post to head home a teasing corner from Craig Bellamy after a period of sustained City pressure, his second goal since his big-money summer transfer from Aston Villa.
Fulham refused to buckle and they were unlucky not to regain the lead in the 78th minute when City keeper Shay Given had to make a fine save to deny Ki-Hyeon Seol.
Carlos Tevez had two headers in the opening period of extra-time, but failed to trouble keeper Stockdale as Fulham's defence held firm.
But the deadlock was finally broken nine minutes before a penalty shoot-out was due to decide the contest when substitute Martin Petrov delivered a perfect far-post corner from which City captain Toure headed home off the underside of the crossbar.