Elano was City's match-winner, scoring a late goal in their third round replay against West Ham United at Eastlands.
With extra-time looming, Elano settled the issue with his seventh goal of the season to earn City a tie at Sheffield United.
In a tightly contested game, a lone goal always looked like settling the outcome and City had the fortune of scoring it.
But it was rough justice on the Hammers as City's Joe Hart was by far the busier of the two keepers.
After an uninspiring opening half-hour, in which neither side created a clear-cut chance, the Hammers almost stole into the lead.
Dean Ashton was put clean through on goal by a diagonal pass from Luis Boa Morte but Hart dashed from his line to make a brilliant block.
City were then forced to make a change when new signing Nery Castillo damaged his left shoulder after falling awkwardly in a challenge with Lucas Neill.
Castillo, captured a fortnight ago on loan from Ukraine club Shakhtar Donetsk, was replaced by Italian Rolando Bianchi.
The Hammers finished the opening half strongly with Lee Bowyer and Anton Ferdinand having attempts at goal though neither troubled Hart who, in stoppage time, again had to dash from his line to make another block to thwart Ashton.
Hart again showed why he is one of England's top young keepers when, early in the second half, he stood up well to keep out an angled shot from Boa Morte.
City had to wait until just short of the hour mark before creating their first scoring attempt of the match when Bianchi, sliding in at the far post, was unable to hit the targets from Martin Petrov's low left-wing cross.
That was followed by a period of City dominance as they became an increasing threat and their efforts were finally rewarded with a goal in the 73rd minute.
Petrov once again opened the Hammers defence on the left and, from his cross, Bianchi headed against the far upright before Elano found the net with a diving header as he reacted first to the loose ball.
Elano had a great chance to seal victory in the dying seconds at a time when the Hammers looked as though they might snatch an equaliser.
Stephen Ireland squared the ball invitingly into the path of the Brazilian but he blazed over from 18 yards when he ought to have hit the target.