Sunderland had taken a 10th-minute lead through on-loan Liverpool striker Fabio Borini and a fine first-half display left them on course for a first piece of major silverware since 1973.
However, City responded in the second half, with Toure lobbing in a superb long-range equaliser and Nasri smashing home less than two minutes later before substitute Jesus Navas added a third goal at the death.
