On the weekend His Highness Sheikh Mansour bin Zayed acquired the 1896–1910 FA Cup trophy, City made light work of the Championship side, delivering a ruthless attacking display full of verve and class.
Bernardo Silva put City ahead on eight minutes with a brilliant left-footed volley from the edge of the area, and the Portuguese midfielder doubled our lead seven minutes later, finishing off a fine team goal with a close-range strike.
Andres Prieto made a fine save from the returning Gabriel Jesus, whose effort from a tight angle lacked the necessary finesse, and Phil Foden thought he was fouled inside the area, but after a quick VAR check, the protests were waved away.
Foden made it 3-0 soon after with a powerful low strike, and only a goalline clearance from Maikel Kieftenbeld denied Jesus inflicting further damage before the half-time break.
City made three changes ahead of the second period, with John Stones and youngsters Felix Nmecha and Taylor Harwood-Bellis coming on to freshen things up.
We remained firmly in control, dictating the game and producing some fine periods of sustained possession, but perhaps lacking the same fluidity we showed in the first 45 minutes.
Our search for a fourth goal was unrelenting. Bernardo flashed an effort wide from Kyle Walker’s cutback as he went in search of his hattrick, and Mahrez’s first-time finish at the backpost was ruled out for offside. It was a very tight call.
A late flurry from the visitors threatened a consolation - Jeremie Bela's stunning effort that skimmed the roof of the net was the closest they came - but City stood firm to record another clean sheet.
Style and substance
City are in a fine run of form.
We’ve won six straight matches in all competitions and are unbeaten in our last 13 - a period that has seen us concede just three goals.
We sit fifth in the Premier League table and in striking distance of top spot, we’ve qualified for the last-16 of the Champions League by winning Group C with a game to spare and have moved through to our fourth-successive Carabao Cup final.
Add our passage to the FA Cup Fourth Round into the mix and, suddenly, our season is shaping up rather nicely.
But aside from the raw numbers, what's perhaps most encouraging is the quality of City's game.
We're working incredibly hard without the ball, not allowing teams to settle for a moment. And when we have possession, we are displaying speed of thought, creativity and ingenuity.
It's an intoxicating mix and teams are struggling to combat it.
If you haven’t yet seen City’s second goal, look out for Riyad Mahrez’s exquisite outside-of-the-boot backspin pass in the buildup.
Man of the match
Two goals, some fine linkup play and plenty of hard-work without the ball, this was Bernardo in full flight.
He shaded the vote just ahead of Foden, who remains a key element of our best attacking moments.
But Kevin De Bruyne was the standout player before he was replaced at half-time by Felix Nmecha.
His vision and range of passing are quite remarkable, and he is surely the best central-midfielder in world football right now.
He's capable of defence-splitting passes seemingly on a whim and the number of times he sliced Birmingham open was frightening.
"Our first objective is done. Some young players were involved and we have qualified for the next round.
"If you follow the trajectory of our team since I arrived, we didn't drop one game. That's why we are in a fourth Carabao Cup final in a row, FA Cup we won two seasons ago, and a semi-final last season.
"Players like Kyle and Gabriel came back. Rodri didn't play last game, Mendy for a long time didn't play.
"So for six, seven players today was good.
"Every game we play, we will try to win and if the players are more or less fresh, I will use them."
Phil Foden has been directly involved in 12 goals in all competitions this season (7 goals & 5 assists), the most of any U21 player for Premier League sides.
What it means
City are in the hat for the fourth round for the ninth-successive season.
The draw for the fourth and fifth rounds takes place on Monday evening live on BT Sport 1 as part of the pre-match coverage ahead of the game between Stockport County and West Ham United.
More information on Monday's draw
We are looking to win the competition for the seventh time, with our last success coming in 2019 as we became the first side in English football history to win all four major men's domestic honours in a single season.
City host Brighton on Wednesday as we look to continue our fine Premier League form.
We have won five and drawn two of our last seven league games and currently sit fifth in the table, four points adrift of leaders Liverpool with two games in hand.
That game kicks off at 6pm UK time, with our minute-by-minute text updates beginning at 4pm and our We're Not Really Here live show getting under way at 5pm.
City XI: Steffen, Cancelo, Walker, Dias, Mendy, Rodrigo, De Bruyne, Bernardo, Foden, Mahrez, Jesus
Subs: Ederson, Stones, Gundogan, Zinchenko, Fernandinho, Delap, Nmecha, Harwood-Bellis, Mbete
Birmingham XI: Prieto, Colin, Clarke-Salter, San Jose, Friend, Sunjic, Kieftenbeld, Sanchez, Toral, Leko, Hogan
Subs: Etheridge, Pedersen, Dean, Dacres-Cogley, Roberts, Clayton, McGree, Bela, Jutkiewicz
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