Stunned by Wigan Athletic in last year's final, City took the lead at Ewood Park through an Alvaro Negredo goal on the stroke of half-time, only for Scott Dann to equalise early in the second period.
City, currently second in the Premier League, also had defender Dedryck Boyata sent off late on for two bookable offences and now face an unwelcome replay against Gary Bowyer's side.
City manager Manuel Pellegrini made seven changes to his starting XI, while former England goalkeeper Paul Robinson returned for Blackburn after spending almost 12 months out due to a blood clot on his lung.
The visitors enjoyed the best of the first half but had to wait until the 45th minute to go ahead, with Negredo volleying home at the back post after Edin Dzeko headed on David Silva's left-wing corner.
City had gone into the game on a run of seven straight wins, but they conceded an equaliser 10 minutes into the second half when Dann pounced after visiting goalkeeper Costel Pantilimon allowed Rudy Gestede's header to bounce off his gloves.
Chris Taylor came close to putting Blackburn in front, while Robinson had to save from Dzeko and substitute Jesus Navas at the other end, before Boyata saw red following an ill-advised swipe at DJ Campbell.
Arsenal host Tottenham Hotspur later on Saturday in the tie of the round, while there are three other all-Premier League fixtures, including Ole Gunnar Solskjaer's first game as Cardiff City manager at Newcastle United.
The day's biggest mismatch sees non-league Macclesfield Town host Championship side Sheffield Wednesday, who sit 63 places above them in the English league system, while Bolton Wanderers play Blackpool in a repeat of the legendary 1953 final.
Holders Wigan begin the defence of their trophy at home to third-tier Milton Keynes Dons.