Manchester City produced a polished performance to outclass Birmingham and reach the FA Cup fourth round.
The hosts were without striker Sergio Aguero, who did not even make the squad despite pre-match promises he would start, but two early goals by Bernardo Silva put them in full control and Phil Foden's strike put the tie beyond doubt before half-time.
Pep Guardiola's side, who beat Manchester United on Wednesday to reach the Carabao Cup final, took things easier in the second half but still dominated possession and gave Bernardo enough chances to complete his hat-trick.
Birmingham were on the back foot from the start, and fell behind when they could only clear Joao Cancelo's clipped pass into the path of Bernardo, who expertly steered the bouncing ball into the top corner with a fierce first-time shot.
Another superb passing move soon after gave Bernardo his second goal, this time with a tap-in from Kevin de Bruyne's pull-back.
The Belgian was in majestic form and opened up the Birmingham defence time and time again before Riyad Mahrez fed Foden to make it 3-0 from the edge of the area.
That advantage was always going to be enough to see off a Birmingham side who are 18th in the Championship and had lost five of their previous six league games, failing to score in the past three.
Birmingham took until the 34th minute to test Zack Steffen through George Friend's deflected shot, but almost got a late consolation when substitute Jeremie Bela blasted just over the bar from 25 yards out.
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