City and Birmingham meet in the FA Cup for the first time since the 1956 Final at Wembley.
Andy Morrison opens the scoring at Maine Road, powering home a header from Danny Tiatto's corner.
Darren Huckerby doubles the lead with a fine solo run before Shaun Goater makes it three before half-time from the spot, after Alife Haaland had been upended by Brum goalkeeper Ian Bennett.
The visitors claw themselves back into the tie after the break with Martin Grainger's impressive curling effort and a Dele Adebola header - but the home side hang on to progress.
Everton gain advantage in the League Cup semi-finals with a 2-1 first-leg victory over City at Goodison Park.
Jesus Navas bags a crucial strike with just under 15 minutes remaining to cancel out Ramiro Funes Mori's opener, but Romelu Lukaku restores the hosts' lead just two minutes later.
The pair are set to meet again at the Etihad Stadium three weeks later...
City cruise into the FA Cup fourth round with an emphatic 5-0 win over West Ham.
Pep Guardiola's men hit our scintillating best in the opening period, as three goals within a 10-minute spell - from Yaya Toure, David Silva and an own-goal from Havard Nordtveit - rip the hosts apart.
City fight back from a goal down to eventually sail past a determined Burnley in the FA Cup third round.
The home side head in at the break trailing to Ashley Barnes' opener but dig deep in the second period with two Sergio Aguero goals in two minutes swinging the game City’s way.
Further efforts from Leroy Sane and sub Bernardo Silva seal a hard-fought, but ultimately impressive win.
City ease into the FA Cup fourth round with a comprehensive victory over Rotherham United.
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